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FOUR COLOR PRINTING 



PRACTICAL PHYSICS 


BY 

HENRY S. CARHART, Sc.D., LL.D. 

v 

FORMERLY PROFESSOR OF PHYSICS, UNIVERSITY OF MICHIGAN 

AND 

HORATIO N. CHUTE, M.S. 

INSTRUCTOR IN PHYSICS IN THE ANN ARBOR HIGH SCHOOL 



5 I 

V. 0 

t> > :> 






ALLYN and BACON 

BOSTON NEW YORK CHICAGO 

ATLANTA SAN FRANCISCO 





QCZ3 

■ C 35 


COPYRIGHT, 1920, BY 
HENRY S. CARHART AND 
HORATIO N. CHUTE 


RDK 



SEP 29 IM) 


Nortooofi yte00 

J. S. Cushing Co. — Berwick & Smith Co. 
Norwood, Mass., U.S.A. 


©CU576670 

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i 


PREFACE 


Practical Physics aims above all things to justify its title. 
In introducing an exceptionally large number of applications, 
the authors have not lost sight of the fact that the most prac¬ 
tical book is the one from which the pupil can most easily 
learn. 

To secure this practical quality, the material is presented in 
the simplest and clearest language: — short sentences and 
paragraphs, terse statements, careful explanations, and an in¬ 
ductive development of each principle. The subject matter 
is logically arranged in the order followed by most secondary 
schools. Each principle is illustrated not only by diagrams, 
problems, and questions, but by its most striking applications. 

While the number of these practical applications is un¬ 
usually large, nothing has been included merely because it is 
sensational; every application illustrates some principle 
treated in the book. The utmost care has been taken to keep 
the whole work within easy range of the average pupil’s ability, 
and to provide material that can be easily mastered in a school 
year. 

The World War has emphasized once more the universality 
of physics. This universality is brought out in Practical 
Physics from the very outset, always, however, with care that 
the pupil understand the basic physical principles which uuder- 
lie each application. 

July 4, 1920. 


iii 


































J 










■ - 




' * 


*«! fei 






































































CONTENTS 


Chapter I. Introduction 

I. Matter and Energy 

II. Properties of Matter . 

III. Physical Measurements 

Chapter II. Molecular Physics 

I. Molecular Motion 

II. Surface Phenomena 

III. Molecular Forces in Solids . 

Chapter III. Mechanics of Fluids 

I. Pressure of Fluids ... 

II. Bodies Immersed in Liquids 

III. Density and Specific Gravity 

IV. Pressure of the Atmosphere 

V. Compression and Expansion of Gases 

VI. Pneumatic Appliances 

Chapter IV. Motion 

I. Motion in Straight Lines . 

II. Curvilinear Motion . 

III. Simple Harmonic Motion . 


1 

6 

16 


25 

29 

34 


39 

53 

58 

65 

73 

83 


. 91 

. 99 

. 101 


Chapter V. Mechanics of Solids 

I. Measurement of Force . . .... 104 

II. Composition of Forces and of Velocities . . . 107 

III. Newton’s Laws of Motion.116 

IV. Gravitation.122 

V. Falling Bodies.128 

VI. Centripetal and Centrifugal Force .... 133 

VII. The Pendulum . . . . . . . . 136 


v 









VI 


CONTENTS 


Chapter VI. Mechanical Work fag* 

I. Work and Energy.143 

II. Machines . . . . . . . . 155 

Chapter VII. Sound 


I. 

Wave Motion .... 




. 176 

II. 

Sound and its Transmission 




. 181 

III. 

Velocity of Sound 




. 184 

IV. 

Reflection of Sound . 




. 186 

V. 

Resonance. 


. 


. 188 

VI. 

Characteristics of Musical Sounds 




. 191 

VII. 

Interference and Beats 




. 194 

VIII. 

Musical Scales .... 




. 196 

IX. 

Vibration of Strings . 




. 201 

X. 

Vibration of Air in Pipes . 




. 205 

XI. 

Graphic and Optical Methods . 



1 

. 208 

Chapter VIII. Light 





I. 

Nature and Transmission of Light 




. 214 

II. 

Photometry .... 




. 219 

III. 

Reflection of Light 




. 223 

IV. 

Refraction of Light . 




. 238 

V. 

Lenses. 




. 246 

VI. 

Optical Instruments . 




. 255 

VII. 

Dispersion. 




. 263 

VIII. 

Color. 




. 271 

IX. 

Interference and Diffraction 




. 276 

Chapter IX. Heat 





I. 

Heat and Temperature 


• 


. 280 

II. 

The Thermometer 


• 


. 282 

III. 

Expansion. 




. 287 

IV. 

Measurement of Heat 




. 297 

V. 

Change of State .... 




. 299 

VI. 

Transmission of Heat 

• 

• 


. 309 

VII. 

Heat and Work .... 

• 

• 


. 319 



















CONTENTS 


Vli 


Chapter X. Magnetism 


I. 

Magnets and Magnetic Action . 

• 

• 

• 

. 327 

II. 

Nature of Magnetism . 

. 

• 

• 

. 332 

III. 

The Magnetic Field . 

. 

. 


. 333 

IV. Terrestrial Magnetism . . 

Chapter XI. Electrostatics 


• 

• 

. 336 

I. 

Electrification .... 





II. 

Electrostatic Induction 


• 


. 344 

III. 

Electrical Distribution 




. 346 

IV. 

Electric Potential and Capacity . 




. 348 

V. 

Electrical Machines 

• 



. 354 

VI. Atmospheric Electricity 

Chapter XII. Electric Currents 

• 

• 

• 

. 358 

I. 

Voltaic Cells .... 





II. 

Electrolysis. 




. 373 

III. 

Ohm’s Law and its Applications 




. 378 

IV. 

Heating Effects of a Current 




. 385 

V. 

Magnetic Properties of a Current 




. 387 

VI. 

Electromagnets .... 




. 392 

VII. 

Measuring Instruments 


• 

• 

. 394 


Chapter XIII. Electromagnetic Induction 

I. Faraday’s Discoveries.401 

II. Self-Induction.405 

III. The Induction Coil . . '! . . . 406 

IV. Radioactivity and Electrons.416 

Chapter XIV. Dynamo-Electric Machinery 


I. Direct Current Machines.421 

II. Alternators and Transformers.431 

III. Electric Lighting.442 

IV. The Electric Telegraph.447 

V. The Telephone.451 

VI. Wireless Telegraphy.453 




















viii CONTENTS 

Chapter XV. The Motor Car page 

I. The Engine ^ . 460 

II. The Storage Battery ....... 466 

III. The Chassis and Running Gear .... 467 

IV. The Brake. .468 

V. The Clutch.469 

VI. Transmission and Differential.470 

VII. The Steering Device.471 

VIII. The Starter ......... 471 

IX. On the Road.472 

X. The Pedestrian.473 

Appendix 

I. Geometrical Constructions.475 

II. Conversion Tables.479 

III. Mensuration Rules. . 481 

IV. Table of Densities.482 

V. Geometrical Construction for Refraction of Light . 483 

Index . ....... 1 


/ 









FULL PAGE ILLUSTRATIONS 




Four Color Process Printing 

Electric Welding .... 
Bureau of Standards, Washington 
Common Crystals . 

Galileo Galilei .... 
Blaise Pascal .... 

Elephant Butte Dam . 

Dry Dock “ Dewey ”... 
Hydro-airplanes .... 
Motion and Force.... 
Sir Isaac Newton .... 
Yosemite Fall .... 
Centrifugal Force .... 
Pisa Cathedral .... 
United States 16-inch Gun . 

Lord Kelvin. 

Lord Rayleigh .... 
Photographs of Sound Waves 

Echo Bridge. 

Hermann von Helmholtz 
Niagara Falls Power Plant . 
Parabolic Mirror at Mount Wilson 
Moving Picture Film . 

Various Spectra .... 
Bridge over the Firth of Forth 
James Watt 
James Prescott Joule . 

A Row of Corliss Engines 
Four-valve Engine 
Section and Rotor of Steam Turbine 
Front and Rear Views of Airplane 
Benjamin Franklin 

ix 


Frontispiece ^ 

FACING PAGE 

. . 16 
. 20 
. 35 

. 42 

. 42 

. 50 

. 58 

. 66 
. 100 
. 124 
. 130 
. 134 
. 136 
. 150 
. 154 
. 182 
. 183 
. 186" 

. 193 
. 214 ^ 

. 236 
. 258 
. 271 
. 291 
. 320 ^ 

. 320 
. 321 
. 322 
. 323 
. 325 
. 358 










X 


FULL PAGE ILLUSTRATIONS 


FACING PAGE 


Hans Christian Oersted . 366 1 

Alessandro Volta.. . . . .382 

Georg Simon Ohm.382 

James Clerk-Maxwell.392 

Joseph Henry.400 

Michael Faraday.401 

Sir William Crookes.412 

Wilhelm Konrad Roentgen . 412 

Madame Curie.418 

Sir Joseph John Thomson.419 

Field Magnet and Drum Armature of D. C. Generator . . 426 

Electric Engine Crossing the Rockies.430 

Armature Core and Field Magnet of A. C. Generator . . 431 
Dam and Power House, Great Falls, Montana .... 438 

Transformers and Switches.439 

Stator and Field of A. C. Generator. 440 

Stator of Three-phase Motor and Motor Complete . . . 441 

Alexander Graham Bell.449 

Samuel F. B. Morse.449 

Field Wireless of the United States Army.452 

Wireless Room in a Transatlantic Liner . . . . . 453 

Heinrich Rudolf Hertz.458 

Thomas Alva Edison.459 

Guglielmo Marconi.459 















PRACTICAL PHYSICS 


CHAPTER I 

INTRODUCTION 

I. MATTER AND ENERGY 

1. Physics Defined. — Physics is the science which treats 
of the related phenomena of matter and energy. It includes 
mechanics, sound, light, heat, magnetism, and electricity. 



A Motor Car. 


Probably the automobile is the best general application of the principles 
of physics. Mechanics of solids is illustrated by its springs, bolts, and most 
of its moving parts ; mechanics of liquids by the circulation of its water¬ 
cooling system ; sound by its horn; light by its headlights; heat by the 
explosions of its engine ; and magnetism and electricity by its electrical 
battery and its starting and lighting systems. 

1 






2 


INTRODUCTION 



Matter and energy scarcely admit of definition except 
by means of their properties. Matter is everything we 
can see, taste, or touch, such as earth, water, wood, iron, 
gas — in short, everything that occupies space. 

Energy is whatever produces a change in the motion or 
condition of matter, especially against resistance opposing 


British “Tank” Crossing a Shell-hole. 

The tank is a land battleship, carrying guns and running on its own track 
which it carries with it. In this way it can cross holes and trenches which 
would stop a vehicle with wheels. 

the change ; that is, energy is the universal agency by means 
of which work is done . Water in an elevated reservoir, 
steam under pressure in a boiler, a flying shell with its 
content of explosives, — all these may do work, may over¬ 
come resistance, or change the position or motion of other 
bodies. They possess energy which is transferred from 
them to the bodies on which work is done. 

2. The Universal Science. — Since everything which we 
recognize by the senses is matter, and every change in 





THE UNIVERSAL SCIENCE 


3 



matter involves energy, it is plain that physics is a uni¬ 
versal science, touching our life at every point. Count¬ 
less physical phenomena are taking place about us every 
day; a girl cooking, a boy playing ball, the fire-whistle 
blowing, the sun giving light and heat, a flag flapping in 
the wind, an airplane soaring aloft, an apple falling from 


A Wright-Martin “ Bomber.” 

An airplane which can cross the United States from coast to coast with 
only one stop. 

a tree, a train or motor car whizzing by, a British “ tank ” 
crossing a shell-hole, — all are examples of matter and 
associated energy. 

Physics is not so much concerned with matter alone or with 
energy alone as with the relations of the two. A baseball is of little 
interest in itself; it becomes interesting only in connection with a 
bat and the energy of the player’s arm. The engine driver’s inter¬ 
est is not so much in the engine itself as in the engine with steam 
up ready to drive it. No one would care to buy an automobile to 




4 


INTRODUCTION 


stand in a garage; its attractiveness lies in the fact that it becomes 
a thing of life when its motor is vitalized by the heat of combustion 
of gasoline vapor. 

3. Applications of the Principles of Physics. — The appli¬ 
cations of the principles of physics in the household 
and in the familiar arts are very numerous and affect us 
constantly in daily life. Water under pressure is deliv¬ 
ered for domestic use, and fuel is used in the liquid or 
in the gaseous form as well as in the solid. Electricity 
lights our houses, toasts our bread, and even cooks our 
daily food. The electric motor runs our vacuum cleaners 
and our sewing machines. 

The applications of physics in modern life are so nu¬ 
merous and they are changing so rapidly that we cannot 
expect to learn about all of them in a year’s study; but 
physical principles remain the same ; and if we acquire a 
knowledge of these principles and of their familiar appli¬ 
cations, we shall be prepared to understand and to ex¬ 
plain other applications that have been made possible by 
the science of physics. 

So this book lays emphasis on the underlying princi¬ 
ples of physics, illustrating them by some of their inter¬ 
esting applications, leaving it to the enthusiasm and 
ingenuity of both teacher and pupils to supplement the 
applications with others drawn from life and from scien¬ 
tific journals. 

4. States of Matter. — Matter exists in three distinct 
states, exemplified by water, which may assume either 
the solid, the liquid , or the gaseous form, as ice, water, or 
water vapor. 

Briefly described, 

Solids have definite size and shape , and offer resistance 
to any change of these. 


FORCE 


5 


Liquids have definite size, but they take the shape of the 
container and have a free surface. 

G-ases have neither definite size nor shape , both depending 
on the container. 

These are not all the differences between solids, liquids, 
and gases, but they serve to distinguish between them. 

Some substances are neither wholly in the one state nor in the 
other. Sealing wax softens by heat and passes gradually from the 
solid to the liquid state. Shoemaker’s wax breaks into fragments like 
a solid under the blow of a hammer, but under long-continued pres¬ 
sure it flows like liquid, though slowly, and it may be molded at will. 



5. Force. — Our primitive idea of force is that of a 
push or a pull; it is derived from experience in making 
muscular exertion to 
move bodies or to 
stop their motion. 

Pushing a chair, 
throwing a stone, 
pulling a cart, row¬ 
ing a boat, stretch¬ 
ing a rubber band, 
bending a bow, 
catching a ball, lift¬ 
ing a book, — all re¬ 
quire muscular ef¬ 
fort in the nature 
of a push or a pull. 

Thus force implies 
a push or a pull, 
though not neces¬ 
sarily muscular; and the effect of the action of a force 
on a body free to move is to give it motion or to change 


A Trip Hammer. 

This weighs several tons and will exert an 
enormous force on the red-hot iron below it. 




INTRODUCTION 


(j 

its motion. For the present we shall make use of the 
units of force familiar to us, such as the pound of force 
and th6 gram of force, meaning thereby the forces equal 
to that required to lift the mass of a pound and that of a 
gram respectively. 

II. PROPERTIES OF MATTER 

6. The Properties of Matter are those qualities that serve 
to define it, as well as to distinguish one substance from 
another. All matter has extension or occupies space, and 
so extension is a general property of matter. On the other 
hand common window glass lets light pass through it, or is 
transparent, while a piece of sheet iron does not transmit 
light, or is opaque. A watch spring recovers its shape 
after bending, or is elastic, while a strip of lead possesses 
this property in so slight a degree that it is classed as in¬ 
elastic. So we see that transparency and elasticity are 
special properties of matter. 

7. Extension. — All bodies have three dimensions, length, 
breadth, and thickness. A sheet of tissue paper or of gold 
leaf, at first thought, appears to have but two dimensions, 
length and breadth; but while its third dimension is rel¬ 
atively small, if its thickness should actually become zero, 
it would cease to be either a sheet of paper or a piece of 
gold leaf. Extension is the property of occupying space or 
having dimensions. 

8. Impenetrability. —While matter occupies space, no 
two portions of matter can occupy the same space at the 
same time. The volume or bulk of an irregular solid, such 
as a lump of coal, may be measured by noting the volume of 
liquid displaced when the solid is completely immersed in it. 
The general property of matter that no two bodies can occupy 
the same space at the same time is known as impenetrability . 


INERTIA 


7 


Put a lump of coal into a tall graduate 
partly filled with water, as in Fig. 1. Note 
the reading at the surface of the water be¬ 
fore and after putting in the coal; the differ¬ 
ence is the volume of water displaced, or the 
volume of the piece of coal. 




CC 

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9. Inertia.— The most conspicuous 
and characteristic general property of 
matter is inertia. Inertia is the prop¬ 
erty which all matter possesses of resist¬ 
ing any attempt to start it if at rest , to 
stop it if in motion , or to change either Figure 1. —Measuring 
the direction or the amount of its motion. VoLUME BY Displacement. 

If a moving body stops, its 
arrest is always owing to 
something outside of itself; 
and if a body at rest is set 
moving, motion must be given 
to it by some other body. It 
is a familiar fact that no body 
of any sort will either start 
or stop moving of itself. 

10. Illustrations of Inertia- — 

Many familiar facts are due to 
inertia. When a street car stops 
suddenly, a person standing con¬ 
tinues by inertia to move forward, 
or is apparently thrown toward the 
front of the car; the driver of a 
racing motor car is apparently 
thrown with violence when the 
rapidly moving car collides with a 
post or a tree ; the fact is the car is 
Figure 2. — Statue Twisted violently stopped, while the driver 
Around by Earthquake. continues to move forward as be- 






















3 


INTRODUCTION 


fore the collision. When a fireman 
shovels coal into a furnace, he suddenly 
arrests the motion of the shovel and 
leaves the coal to move forward by 
inertia. A smooth cloth may be 
snatched from under a heavy dish with¬ 
out disturbing it. The violent jar to a 
water pipe when a faucet is quickly 
closed is accounted for by the inertia 
of the stream. Tall columns, chimneys, 
and monuments are sometimes twisted 
around by violent earthquake move¬ 
ments (Fig. 2). The sudden circular 
motion of the earth under a column 
leaves it standing still, while the slower 
return motion carries it around. The 
persistence with which a spinning top 
maintains its axis of rotation in the same 
direction is due to its inertia. If it is 
spun on a smooth surface, like a mirror, 
and is tossed into the air, it will not 
tumble over and over, but.will keep upright (Fig. 3) and may be 
caught on the mirror, still spin- 



Figure 3. — Spinning Top 
Maintains Its Axis of Ro¬ 
tation. 


ning on its point. The gyrostat 
wheel acts on the same principle, 
and so does Sperry’s gyrostatic 
compass and his stabilizer for 
ships and aeroplanes. 

If a round flat biscuit is pitched 
into the air, there is no certainty 
as to how it will come down; but 
if it is given a spin before it 
leaves the hand, the axis of spin¬ 
ning keeps parallel to itself (Fig. 
4). If one wants to throw a hoop 
or a hat to some one to catch on 
a stick, one gives to the hoop or 
the hat a spin. So also if one 
wants to throw a quoit and be 


f\ 

V\ 


o 


© 



Figure 4. — Spinning Biscuit. 




MASS 


9 


certain how it will alight, one gives it a spin. Its inertia keeps it 
spinning around the same axis in space. 

Tie a piece of twine to a heavy weight, such as a flatiron. By pull¬ 
ing slowly the flatiron may be lifted, but a sudden jerk on the twine 
will break it because of the inertia of the weight. 

Suspend a heavy weight by a cotton string, as in 
Fig. 5, and tie a piece of the same string to the 
under side of the weight. A steady downward pull 
at B will break the upper string because it carries the 
greater load. A sudden downward pull on B will 
break the lower string before the pull reaches the 
upper one on account of the inertia of the weight. 

11. Mass.-—We are all familiar with the 
fact that the less matter there is in a body, 
the more easily it is moved, and the more Figure 5. — 
easily it is stopped when in motion. One ExpERI ' 

can tell an empty barrel from a full one by a 
kick, a block of wood from a brick by shoving it with the 
foot, and a tennis ball from a baseball by catching it. 
The mass of a body is the quantity of matter it contains ; 
but since the inertia of a body is proportional to the 
quantity of matter in it, it is not difficult to see that the 
mass of a body is the measure of its inertia . 

While mass is most easily measured by means of weigh¬ 
ing, it must not be confused with weight (§ 132), because 
mass is independent of the earth-pull or gravity. The 
mass of a meteoric body is the same when flying through 
space as when it strikes the earth and embeds itself in the 
ground. If it could reach the center of the earth, its 
weight would become zero; at the surface of the sun it 
would weigh nearly twenty-eight times as much as at the 
earth’s surface; but its mass would be the same every¬ 
where. For this reason, and others which will appear 
later, in discussing the laws of physics we prefer to speak 




10 


INTRODUCTION 



of mass when a student thinks the term weight might be 
used as well. 

12. Cohesion and Adhesion. — All bodies are made up of 
very minute particles, which are separately invisible, and 

are called mole¬ 


cules. Cohesion 
is the force of at¬ 
traction between 
molecules, and it 
binds together 
the molecules of 
a substance so as 
to form a larger 
mass than a mol¬ 
ecule. Adhe¬ 
sion is the force 
uniting bodies by 
their adjacent 
surfaces . When 
two clean sur¬ 
faces of white- 
hot wrought 
iron are brought 
into close con¬ 
tact by hammer¬ 
ing, they cohere 
and become a 
single body. If 
a clean glass rod 

be dipped into water and then withdrawn, a drop will ad¬ 
here to it. Glue, adhesive plaster, and postage stamps 
stick by adhesion. Mortar adheres to bricks and nickel 
plating to iron. 


Cohesion. 

Mr. Lambirth, dean of blacksmiths in America, 
has spent 35 years at the head of the forge work at 
the Massachusetts Institute of Technology. 








POLiOSITY % 


11 


Suspend from one of the arms of a beam balance a clean glass disk 
by means of threads cemented to it (Fig. 6). After counterpoising 
the disk, place below it a vessel of water, and adjust so that the disk 
just touches the surface of the water when the beam of the balance is 
horizontal. Now add weights to the opposite pan until the disk is 
pulled away from the water. Note that the under surface of the disk 
is wet. The adhesion of the 
water to the glass is greater 
than the cohesion between 
the molecules of the water. 

If lycopodium powder be 
carefully sifted on the sur¬ 
face of the water, the water 
will not wet the disk and 
there will be no adhesion. 

If mercury be substituted for 
water, a much greater force 
will be necessary to separate 
the disk from the mercury, 
but no mercury will adhere 
to it. The force of cohesion 
between the molecules of the 
mercury is greater than the adhesion between it and the glass. 

Cut a fresh, smooth surface on each of two lead bullets and hold 
these surfaces gently together. They will not stick. Now press them 
tightly together with a slight twisting motion. They will adhere 
quite firmly. This fact shows that molecular forces act only through 
insensible distances. It has been shown that they vanish in water at 
a range of about one five-hundred-thousandth of an inch. 

An interesting example of selective adhesion occurs in the winning 
of diamonds in south Africa. The mixed pebbles and other worthless 
stones, with an occasional diamond, are washed down an inclined 
shaking surface covered with grease. Only the diamonds and a few 
other precious stones stick to the grease; the rest are washed away. 

13. Porosity. — Sandstone, unglazed pottery, and similar 
bodies absorb water without change in volume. The water 
fills the small spaces called pores , which are visible either 
to the naked eye or under a microscope. All matter is 























12 


INTRODUCTION 


probably porous, though the pores are invisible, and the 
corresponding property is called porosity. In a famous 
experiment in Florence many years ago, a hollow sphere 
of heavily gilded silver was filled with water and put 
under pressure. The water came through the pores of the 
silver and gold and stood in beads on the surface. Francis 
Bacon observed a similar phenomenon with a lead sphere. 

Oil penetrates into marble and spreads through it. Even so dense 
a snbstance as agate is porous, for it is artificially colored by the ab¬ 
sorption, first of one liquid and then of another which acts chemically 
on the first; the result is a deposit of coloring matter in the pores of 
the agate. 

14. Tenacity and Tensile Strength. — Tenacity is the resist¬ 
ance which a body offers to being torn apart. The tensile 

, strength of wires is tested by hanging them 

vertically and loading with successive weights 
until they break (Fig. 7). The breaking 
weights for wires of different materials but of 
the same cross section differ greatly. A knowl¬ 
edge of tensile strength is essential in the de¬ 
sign of telegraph wires and cables, suspension 
bridges, and the tension members of all steel 
structures. 

Tenacity diminishes with the duration of the 
pull, so that wires sometimes break with a load 
which they have supported for a long time. 
— 1 ^Tensile Lead ^ as the l eas t tenacity of all solid metals, 
Strength and cast steel the greatest. Even the latter is 
of Wire. excee( j e( j fiy fibers of silk and cotton. Single 
fibers of cotton can support millions of times their own 
weight. 

15. Ductility. —Ductility is the property of a substance 
which permits it to be drawn into wires or filaments . Gold, 










TENACITY AND TENSILE STRENGTH 


13 



copper, silver, and platinum are highly ductile. The last 
is the most ductile of all. It has been drawn into wire 
only 0.00003 inch in diameter. A mile of this wire would 
weigh only 1.25 grains. 


Aerial Tramway over the Whirlpool Rapids. 

The cables have great tensile strength to support the car. 

Other substances are highly ductile only at high tem¬ 
peratures. Glass has been spun into such fine threads 
that a mile of it would weigh only one third of a grain. 
Melted quartz has been drawn into threads not more than 
0.00001 inch in diameter. Such threads have nearly as 
great tenacity as steel. 




14 


INTRODUCTION 


16. Malleability. — Malleability is a property which per¬ 
mits of hammering or rolling some metals into thin sheets. 

Gold leaf, made by- 
hammering between 
skins, is so thin that 
it is partially trans¬ 
parent and trans¬ 
mits green light. 
Zinc is malleable 
when heated to a 
temperature of from 
100° to 150° C. 
(centigrade scale). 
It can then be rolled 
into sheets. Nickel 
at red heat can 
be worked like 
wrought iron. Mal¬ 
leable iron is made 
from cast iron by 
heating it for sev¬ 
eral days in contact with a substance which removes some 
of the carbon from the cast iron. 

17. Hardness and Brittleness. — Hardyiess is the resistance 
offered by a body to scratching by other bodies. The relative 
hardness of two bodies is ascertained by finding which will 
scratch the other. Diamond is the hardest of all bodies 
because it scratches all others. Sir William Crookes has 
shown that diamonds under great hydraulic pressure be¬ 
tween mild steel plates completely embed themselves in 
the metal. Carborundum, an artificial material used for 
grinding metals, is nearly as hard as diamond. 

Brittleness is aptness to break under a blow. It must be 






HARDNESS AND BRITTLENESS 


15 


distinguished from hardness. Steel is hard and tough, 
while glass is hard and brittle. 

Tool steel becomes glass-hard and brittle when suddenly 
cooled from a high temperature. The tempering of steel 
is the process of giving the degree of hardness required 
for various purposes. It consists usually in first plunging 
the article at red heat into cold water or other liquid to 
give it an excess of hardness; then reheating gradually 
until the hardness is reduced, or “ drawn down,” to the 
required degree. The indication of the hardness is the 
color appearing on a polished portion, such as straw- 
yellow, brown-yellow, purple, or blue. 

The process of annealing as applied to iron and glass is used to 
render them less brittle. It is done by cooling very slowly and uni¬ 
formly from a high temperature. Soft iron is thus made more ductile, 
while glass is relieved from the molecular stresses set up in rapid 
cooling, and it thus becomes tougher and more uniform. The best 
lamp chimneys are annealed by the manufacturer. Disks of glass for 
telescope lenses and mirrors must be carefully annealed to prevent 
fracture and warping during the process of grinding and polishing. 

Prince Rupert drops (Fig. 8) are made by dropping melted glass 
into cold water. The outside is suddenly chilled and solidified, while 
the interior is still fused, and when it cools it must ac¬ 
commodate itself to the dimensions of the outer skin. 

The drop is thus under great tension. With a pair 
of pliers break off the tip of the drop under water 
in a tumbler, or scratch with a file; the whole drop 
will fly to powder with almost explosive violence. 

A large tall jar on foot is usually thick at the bot- RuPERT 

tom, and imperfectly annealed. Such jars have not 
infrequently been broken by a scratch inside, made, for example, by 
stirring emery powder in water by means of a long wooden stick. 
A scratch inside is usually fatal to a lamp chimney. 

A large glass tube may be cut in two by scratching it around on the 
inside by means of an appropriate tool, and then carefully heating it 
in a small gas flame. 



Figure 8.— 


16 


INTRODUCTION 


Exercises 

1. Given a large crystal of rock candy. Can its volume be deter¬ 
mined by the method outlined under impenetrability ? How ? 

2. The volume of a bar of lead can be reduced by pounding it. 
Explain. 

3. A small quantity of sugar can be dissolved in a cup of water 
without increasing the volume. Explain. 

4. A quick blow with a heavy knife will often remove smoothly 
the neck of a glass bottle, while a less vigorous blow will shatter the 
bottle. Explain. 

5. Why can an athlete jump farther in a running jump than in 
a standing jump ? 

6. By striking the end of the handle it can be driven into a heavy 
ax much better than by pounding the ax. Why ? 

7. A man standing on a flat-bottomed car that is moving jumps 
vertically upward. Will he come down on the spot from which he 
jumped ? Explain. 

8. If a top be set spinning it stands up; if not spinning it topples 
over. Explain. 

9. A bullet fired from a rifle will pass through a pane of glass, 
cutting a fairly smooth hole; a stone thrown by the hand on striking 
a pane of glass will shatter it. Explain. 

10. Name three properties of matter that are characteristic of it. 

11 . A rolling wheel does not fall over, but one not rolling topples 
over. Why ? 

12. Why hold a heavy hammer against a spring board when driv¬ 
ing a nail into it? 

13. In Jules Verne’s Trip to the Moon the incident is told that 
when a few days on the way the dog died and was thrown overboard. 
To their surprise the dead dog followed along after them. Is Verne’s 
Physics correct ? Explain. 

II. PHYSICAL MEASUREMENTS 

18. Units. — To measure any physical quantity a certain 
definite amount of the same kind of quantity is used as the 
unit. For example, to measure the length of a body, some 



Electric Welding 










MEASURES OF LENGTH 


17 


arbitrary length, as a foot, is chosen as the unit of length; 
the length of a body is the number of times this unit is con¬ 
tained in the longest dimension of the body. The unit is 
always expressed in giving the magnitude of any physical 
quantity; the other part of the expression is the numerical 
value. For example, 60 feet, 500 pounds, 45 seconds. 

In like manner, to measure a surface, the unit, or stand¬ 
ard surface, must be given, such as a square foot; and to 
measure a volume, the unit must be a given volume, such, 
for example, as a cubic inch, a quart, or a gallon. 

19. Systems of Measurement. — Commercial transactions in 
most civilized countries are carried on by a decimal system 
of money, in which all the multiples are ten. It has the 
advantage of great convenience, for all numerical operations 
in it are the same as' those for abstract numbers in the dec¬ 
imal system. The system of weights and measures in use 
in the British Isles and in the United States is not a dec¬ 
imal system, and is neither rational nor convenient. On 
the other hand most of the other civilized nations of the 
world within the last fifty years have adopted the metric 
system , in which the relations are all expressed by some 
power of ten. The metric system is in well-nigh universal 
use for scientific purposes. It furnishes a common numer¬ 
ical language and greatly reduces the labor of computation. 

20. Measures of Length. — In the metric system the unit 
of length is the meter. In the United States it is the dis¬ 
tance between two transverse lines on each of two bars of 
platinum-iridium at the temperature of melting ice. These 
bars, which are called “national prototypes,” were made 
by an international commission and were selected by lot 
after two others had been chosen as the “ international pro¬ 
totypes * for preservation in the international laboratory 
on neutral ground at Sevres near Paris. Our national 


18 


INTRODUCTION 


prototypes are preserved at the Bureau of Standards in 
Washington. Figure 9 shows the two ends of one of 
them. The only multiple of the meter in general use is the 
kilometer , equal to 1000 meters. It is used to measure such 
distances as are expressed in miles in the English system. 



Figure 9. — Ends of Meter Bar. 


The Common Units in the Metric System are : 

1 kilometer (km.) = 1000 meters (m.) 

1 meter = 100 centimeters (cm.) 

1 centimeter =10 millimeters (mm.) 

The Common Units in the English System are: 

1 mile (mi.) = 5280 feet (ft.) 

1 yard (yd.) = 3 feet 
1 foot = 12 inches (in.) 

By Act of Congress in 1866 the legal value of the yard 
is f-ffy meter; conversely the meter is equal to 39.37 
inches. The inch is, therefore, equal to 2.540 centimeters. 

100 MILLIMETERS = 10 CENTIMETERS = 1 DECIMETER =3.937 INCHES. 



U_ 2 3| 4 

INCHES AND TENTHS 

Figure 10. — Centimeter and Inch Scales. 

The unit of length in the English system for the United 
States is the yard , defined as above. The relation between 
the centimeter scale and the inch scale is shown in Fig. 10. 






























CUBIC MEASURE 


19 


Cm. 


21. Measures of Surface. — In the metric system the unit 
of area used in the laboratory is the square centimeter 
(cm. 2 ). It is the area of a square, the edge of which is 
one centimeter. The square meter (m. 2 ) is often em¬ 
ployed as a larger unit of area. In the 
English system both the square inch 
and the square foot are in common use. 

Small areas are measured in square 
inches, while the area of a floor and 
that of a house lot are given in 
square feet; larger land areas are in 
acres, 640 of which are contained in a 
square mile. 

The square inch contains 2.54 x 2.54 
= 6.4516 square centimeters. The relative sizes of the 
two are shown in Fig. 11. 


Square inch 


Figure 11. — 
Square Centimeter 
and Square Inch. 


The area of regular geometric figures is obtained by computation 
from their linear dimensions. Thus the area of a rectangle or of a 
parallelogram is equal to the product of its 
base and its altitude (A = b x h ); the area 
of a triangle is half the product of its base 
and its altitude (A =\b x h) ; the area of a 
circle is the product of 3.1416 (very nearly 
*yf) and the square of the radius (A = 7rr 2 ) ; 
the surface of a sphere is four times the area 
of a circle through its center (A = 47rr 2 ). 
For other surfaces, see Appendix III. 

22. Cubic Measure. — The smaller 

Figure 12. — Cubic ull it of volume in the metric system 

Centimeter and Cubic . ^ ^ centimeter. It is the vol- 

Inch. 

ume of a cube, the edges of which are 
one centimeter long. The cubic inch equals (2.54) 3 or 
16.387 cubic centimeters. The relative sizes of the two 
units are shown in Fig. 12. In the English system the 


















20 


INTRODUCTION 



Figure 13. 
— Cylindri¬ 
cal Glass 
Graduate. 


cubic foot and cubic yard are employed for 
larger volumes. The cubical capacity of a 
room or of a freight car would be expressed 
in cubic feet; the volume of building sand 
and gravel or of earth embankments, cuts, 
or fills would be in cubic yards. 

The unit of capacity for liquids in the 
metric system is the liter. It is a decimeter 
cube, that is, 1000 cubic centimeters. The 
imperial gallon of Great Britain contains 
about 277.3 cubic inches, and holds 10 
pounds of water at a temperature of 62° 
Fahrenheit. The United States gallon has 
the capacity of 231 cubic inches. 

Common Units in the Metric Sys¬ 
tem : 


1 cubic meter (m. 3 ) = 1000 liters (1.) 

1 liter = 1000 cubic centimeters (cm. 3 ) 


Common Units in the English System: 

1 cubic yard (cu.yd.)= 27 cubic feet (cu. ft.) 

1 cubic foot = 1728 cubic inches (cu. in.) 

1 U. S. gallon (gal.) = 4 quarts (qt.) = 231 cubic inches 
1 quart = 2 pints (pt.) 


The volume of a regular solid, or of a solid geometrical figure, may 
be calculated from its linear dimensions. Thus, the number of cubic 
feet in a room or in a rectangular block of marble is found by get¬ 
ting the continued product of its length, its breadth, and its height, 
all measured in feet. The volume of a cylinder is equal to the product 
of the area of its base (7rr 2 ) and its height, both measured in the 
same system of units. 

Liquids are measured by means of graduated vessels of metal or of 
glass. Thus, tin vessels holding a gallon, a quart, or a pint are used 




United States Bureau of Standards. 















UNITS OF MASS 


21 



for measuring gasoline, sirup, etc. Bottles for acids usually hold 
either a gallon or a half gallon, and milk bottles contain a quart, a 
pint, or a half pint. Glass cylindrical graduates (Fig. 

13) and volumetric flasks (Fig. 14) are used by phar¬ 
macists, chemists, and physicists to measure liquids. 

In the metric system these are graduated in cubic cen¬ 
timeters. 


Figure 14. 
—Volumetric 
Flask. 


23. Units of Mass. — The unit of mass in 
the metric system is the kilogram. The 
United States has two prototype kilograms 
made of platinum-iridium and preserved at 
the Bureau of Standards in Washington 
(Fig. 15). The gram is one thousandth of 
the kilogram. The latter was originally de¬ 
signed to represent the mass of a liter of 
pure water at 4° C. (centigrade scale). For 
practical purposes this is the kilogram. The 
gram is therefore equal to the mass of a cubic centimeter 
of water at the same temperature. The mass of a given 

body of water can 
thus be immediately 
inferred from its vol¬ 
ume. 

The unit of mass in 
the English system is 
the avoirdupois pound. 
The ton of 2000 pounds 
is its chief multiple ; 
its submultiples are the 
ounce and the grain. 
The avoirdupois pound 
is equal to 16 ounces 
Figure 15 . — Standard Kilogram. and to 7000 grains. 













22 


INTBODUCTION 


The u troy pound of the mint ” contains 5760 grains. In 
1866 the mass of the 5-cent nickel piece was legally fixed 
at 5 grams ; and in 1873 that of the silver half dollar at 
12.5 grams. One gram is equal approximately to 15.432 
grains. A kilogram is very nearly 2.2 pounds. More 
exactly, one kilogram equals 2.20462 pounds. 

All mail matter transported between the United States and the fifty 
or more nations signing the International Postal Convention, including 
Great Britain, is weighed and paid for entirely by metric weight. 
The single rate upon international letters is applied to the standard 
weight of 15 grams or fractional part of it. The International Parcels 
Post limits packages to 5 kilograms; hence the equivalent limit of 
11 pounds. 

Common Units in the English System: 

1 ton (T.) = 2000 pounds (lb.) 

1 pound = 16 ounces (oz.) 

1 ounce = 437.5 grains (gr.) 

Common Units in the Metric System : 

1 kilogram (kg.) = 1000 grams (g.) 

1 gram = 1000 milligrams (mg.) 

24. The Unit of Time. — The unit of time in universal 
use in physics and by the people is the second. It is 
a mean solar day. The number of seconds be¬ 
tween the instant when the sun’s center crosses the me¬ 
ridian of any place and the instant of its next passage 
over the same meridian is not uniform, chiefly because 
the motion of the earth in its orbit about the sun varies 
from day to day. The mean solar day is the average 
length of all the variable solar days throughout the year. 
It is divided into 24 x 60 x 60 = 86,400 seconds of mean 
solar time, the time recorded by clocks and watches. 


PROBLEMS 


23 


The sidereal day used in astronomy is nearly four minutes 
shorter than the mean solar day. 

25. The Three Fundamental Units. — Just as the meas¬ 
urement of areas and of volumes reduces simply to the 
measurement of length, so it has been found that the 
measurement of most other physical quantities, such as 
the speed of a ship, the pressure of water in the mains, 
the energy consumed by an electric lamp, and the horse 
power of an engine, may be made in terms of the units of 
length , mass , and time. For this reason these three are 
considered fundamental units to distinguish them from all 
others, which are called derived units. 

The system now in general use in the physical sciences 
employs the centimeter as the unit of length, the gram, as 
the unit of mass, and the second as the unit of time. It 
is accordingly known as the c. g. s. (centimeter-gram- 
second) system. 


Problems 

In solving these problems the student should use the relations and 
values given in §§ 20, 22, and 23. 

1. Reduce 76 cm. to its equivalent in inches. 

2. Express in feet the height of Eiffel Tower, 355 m. 

3. The metric ton is 1000 kg. Find the difference between it and 
an American ton. 

4. If milk is 15 cents a quart, what would be the price per liter? 

5. On the basis that one liter of water weighs a kilogram, what 
would a gallon of water weigh in pounds ? 

6. What per cent larger than a pound avoirdupois is half a 
kilogram ? 

7. If the speed limit on a state road is 25 mi. per hour, what would 
that be expressed in kilometers per hour ? 

8. How many liters in a cubic foot of water? 


24 


INTRODUCTION 


9 . What is the equivalent in the metric system of a velocity of 
1090 ft. per second ? 

10. If a cylindrical jar is 4 in. in diameter and one foot deep, how 
many liters will it hold ? 

11. Express the velocity of light, 186,000 miles per second, in 
kilometers per second. 

12. What would be the error made if in measuring 12 ft. a bar 
30 cm. long is used as a foot ? 

13 . If a cubic foot of water weighs 62.4 lb., what would a pint of 
water weigh? 

14 . If coal sells at $12 per ton, what would 20,000 kilograms cost? 


CHAPTER II 


MOLECULAR PHYSICS 
I. MOLECULAR MOTION 

26. Diffusion of Gases. — If two gases are placed in free 
communication with each other and are left undisturbed, 
they will mix rather rapidly. Even though they differ in 
density and the heavier gas is at the bottom, the mixing 
goes on. This process of the spontaneous mixing of gases 
is called diffusion. 

The rapidity with which gases diffuse may be illus¬ 
trated by allowing illuminating gas to escape into a room, 
or by exposing ammonia in an open dish. The odor 
quickly reveals the presence of either gas in all parts of 
the room, even when air currents are suppressed as far as 
possible. A more agreeable illustration is furnished by a 
bottle of smelling salts. If it is left 
open, the perfume soon pervades the 
whole room. 

Fill one of a pair of jars (Fig. 16) with the 
fumes of strong hydrochloric acid, and the 
other with gaseous ammonia, and place over 
them the glass covers. Bring the jars together 
as shown, and after a few seconds slip out the 
cover glasses. In a few minutes both jars will 
be filled with a white cloud of the chloride 
of ammonia. Instead of these vapors, air and 
illuminating gas may be used, and after dif¬ 
fusion, the presence of an explosive mixture in both jars may be 
shown by applying a flame to the mouth of each separately. 

26 



Figure 16 .—Diffusion 
of Gases 




26 


moleculAb PHYSIC8 


27. Effusion through Porous Walls. —The passage of a 
gas through the pores of a solid is known as effusion. 
The rate of effusion for different gases is nearly inversely 

proportional to the square root of their 
relative densities. Hydrogen, for ex¬ 
ample, which is one sixteenth as heavy as 
oxygen, passes through very small open¬ 
ings four times as fast as oxygen. 

Cement a small unglazed battery cup to a funnel 
tube, and connect the latter to a flask nearly filled 
with water and fitted with a jet tube, as shown in 
Fig. 17. Invert over the porous cup a large glass 
beaker-or bell jar, and pass into it a stream of hy¬ 
drogen or illuminating gas. If all the joints are 
air-tight, a small water jet will issue from the fine 
tube. The hydrogen passes freely through the in¬ 
visible pores in the walls of the porous cup and 
produces gas pressure in the flask. If the beaker 
is now removed, the jet subsides and the pressure 
in the flask quickly falls to that of the air outside 
by the passage of hydrogen outward through the pores of the cup. 

28. Molecular Motion in Gases. — The simple facts of the 
diffusion and effusion of gases lead to the conclusion that 
their molecules (§ 12) are not at rest, but are in constant 
and rapid motion. The property of indefinite expansibility 
is a further evidence of molecular motion in gases. No 
matter how far the exhaustion is carried by an air pump, 
the gas remaining in a closed vessel expands and fills it. 
This is not due to repulsion between the molecules, but 
to their motions. Gases move into a good vacuum much 
more quickly than they diffuse through one another. In 
diffusion their motion is frequently arrested by molecular 
collisions, and hence diffusion is impeded. 

The property of rapid expansion into a free space is a 



Figure 17. — 
Effusion of Hy¬ 
drogen. 








THE VELOCITY OF MOLECULES 


27 



highly important one. The operation of a gasoline engine, 
in which the inlet valve presents only a narrow opening 
for a small fraction of a second, is an excellent illustration ; 
and yet this brief period suffices for the explosive mixture 
to enter and fill the 


cylinder , 

29. Pressure Produced 
by Molecular Bombard¬ 
ment. — It would be 
possible to keep an iron 
plate suspended hori¬ 
zontally in the air by 
the impact of a great 
many bullets fired up 
against its under sur¬ 
face. The clatter of an 
indefinitely large num¬ 
ber of hailstones on a 
roof forms a continuous 
sound, and their fall 
beats down a field of 
grain flat to the ground. 

So the rapidly moving 
molecules of a gas strike 
innumerable minute 
blows against the walls 
of the containing vessel, and these blows compose a con¬ 
tinuous pressure. This, in brief, is the kinetic theory of 
the pressure of a gas. 

30. The Velocity of Molecules. — It has been found pos¬ 
sible to calculate the velocity which the molecules of air 
must have under standard conditions to produce by their 
impact against the walls of a vessel the pressure of one 


Cross Section of Automobile Motor. 

The valve V is open only a fraction of a 
second, but the gas fills the cylinder C 
completely. 





28 


MOLECULAR PHYSICS 


atmosphere, or 1088 g. per square centimeter. It is about 
450 m. per second. For the same pressure of hydrogen, 
which is only one fourteenth as heavy as air, the velocity 
has the enormous value of 1850 m. per second. The high 
speed of the hydrogen molecules accounts for their rela¬ 
tively rapid progress through porous walls. 

31. Diffusion of Liquids. — Liquids diffuse into one an¬ 
other in a manner similar to that of gases, but the 
process is indefinitely slower. Diffusion in 
liquids, as in gases, shows that the molecules 
have independent motion because they move 
more or less freely among one another. 

Let a tall jar be nearly filled with water colored with 
blue litmus, and let a little strong sulphuric acid be intro¬ 
duced into the jar at the bottom by means of a thistle tube 
(Fig. 18). The density of the acid is 1.8 times that of the 
litmus solution, and the acid therefore remains at the bot¬ 
tom with a well-defined surface of separation, which turns 
red on the litmus side because acid reddens litmus. But 
if the jar be left undisturbed for a few hours, the line of 
separation will lose its sharpness and the red color will 
move gradually upward, showing that the acid molecules have made 
their way toward the top. 



32. Diffusion of Solids. — The diffusion of solids is much 
less pronounced than the diffusion of gases and liquids, but 
it is known to occur. Thus, if gold be overlaid with lead, 
the presence of gold throughout the lead may in time be 
detected. Mercury appears to diffuse through lead at 
ordinary temperatures; in electroplating the deposited 
metal diffuses slightly into the baser metal; at higher 
temperatures metals diffuse into one another to a marked 
degree, so that there is evidence of molecular motion in 
solids also. 




MOLECULAR FORCES IN LIQUIDS 


29 


II. SURFACE PHENOMENA 


33. Molecular Forces in Liquids. — By an easy transition 
of ideas we carry the primitive conception of force derived 
from the sense of muscular exertion over to forces other 


than those exerted by men and animals, such as those be¬ 
tween the molecules of a body. Molecular forces act only 
through insensible distances, such as the distances separat¬ 
ing the molecules of solids and liquids. A clean glass 
rod does not attract water until there is 
actual contact between the two. If the 
rod touches the water, the latter clings 
to the glass, and when the rod is with¬ 
drawn, a drop adheres to it. If the drop 
is large enough, its weight tears it away, 
and it falls as a little sphere. 



By means of a pipette a large globule of olive Figure 19.— 
oil may be introduced below the surface of a Spherical Globule 
mixture of water and alcohol, the mixture having 
been adjusted to the same density (§ 69) as that of the oil by varying 
the proportions. The globule then assumes a truly spherical form and 
floats anywhere in the mixture (Fig. 19). 

Cover a smooth board with fine dust, such as lycopodium powder 
or powdered charcoal. If a littlo water be dropped upon it from a 

height of about two 
feet, it will scatter and 
take the form of little 
spheres (Fig. 20). 

In all these illus¬ 
trations the spheri- 

Figure 20. -Spherical Drops of Water. Qal form ig ac _ 



counted for by the forces between the molecules of the 
liquid. They produce uniform molecular pressure and 
form little spheres, because a spherical surface is the 
smallest that will inclose the given volume. 














30 


MOLECULAR PHYSICS 


34. Condition at the Surface of a Liquid. — Bubbles of gas re¬ 
leased in the interior of a cold liquid and rising to the surface often 
show some difficulty in breaking through. A sewing needle carefully 
placed on the surface of water floats. The water around the needle is 
depressed and the needle rests in a little hollow 
(Fig. 21). 

Let two bits of wood float on water a few mil¬ 
limeters apart. If a drop of alcohol is let fall on 
the water between them, they suddenly fly apart. 

A thin film of water may be spread evenly 
over a chemically clean glass plate; but if the 
film is touched with a drop of alcohol on a thin 
glass rod, the film will break, the water retiring and leaving a dry 
area around the alcohol. 



Figure 21. — 
Needle Floating on 
Water. 


The sewing needle indents the surface of the water as if 
the surface were a tense membrane or skin, and tough enough 
to support the needle. This surface skin is weaker in alcohol 
than in water; hence the bits of wood are pulled apart and 
the water is withdrawn from the spot weakened with alcohol. 

35. Surface Tension. — The molecules composing the 


surface of a liquid are not under the same conditions of 
equilibrium as those within the liquid. The latter are 
attracted equally in all directions r 

by the surrounding molecules, while 
those at the surface are attracted 
downward and laterally, but not up¬ 
ward (Fig. 22). The result is an 
unbalanced molecular force toward 
the interior of the liquid, so that 
the surface layer is compressed and 
tends to contract. The contraction 

means that the surface acts like a stretched membrane, 
which molds the liquid into a volume with as small a 
surface as possible. Liquids in small masses, therefore, 
always tend to become spherical. 



Figure 22. — Molecular 
Attractions. 















ILLUSTRATIONS 


31 





36. Illustrations. — Tears, 

dewdrops, and drops of rain are 
spherical because of the tension in 
the surface film. Surface tension 
rounds the end of a glass rod or 
stick of sealing wax when softened 
in a flame. It breaks up a small 
stream of molten lead into little 
sections, and molds them into 
spheres which cool as they fall and 


Figure 23. — Circle in Liquid Film. 


Figure 24. — 
Plane Films. 


form shot. Small globules of mer¬ 
cury on a clean glass plate are slightly flattened by their weight, 
but the smaller the globules the more nearly spherical they are. 

Of stout wire make a ring three or four inches in 
diameter with a handle (Fig. 23). Tie to it a loop 
of soft thread so that the loop may hang near the 
middle of the ring. Dip the ring into a soap solu¬ 
tion containing glycerine, and get a plane film. The 
thread will float in it. Break the film inside the loop 
with a warm pointed wire, and the loop will spring 
out into a circle. The tension of the film attached 
to the thread pulls it out equally in all directions. 

Interesting surfaces may be obtained by dipping 
skeleton frames made of stout wire into a soap solu¬ 
tion. The films in Fig. 24 are all plane, and the angles where 
three surfaces meet along a line are necessarily 120° for equilibrium. 

A bit of gum camphor on warm water, quite free from an oily film, 
will spin around in a 
most erratic manner. 

The camphor dissolves 
unequally at different 
points, and thus pro¬ 
duces unequal weaken¬ 
ing of [the surface ten 
sion in different direc¬ 
tions. 

Make a tiny wooden 
boat and cut a notch in 
the stern ; in this notch 


Figure 25. — Boat Drawn by Surface Tension. 




































MOLECULAR PHYSICS 

put a piece of camphor gum (Fig. 25). The cam¬ 
phor will weaken the tension astern, while the ten¬ 
sion at the bow will draw the boat forward. 

Surface tension makes a soap bubble contract. 
Blow a bubble on a small funnel and hold the open 
tube near a candle flame (Fig. 26). The expelled 
air will blow the flame aside, and the smaller the 
bubble the more energetically will it expel the air. 

A small cylinder of fine wire gauze with solid 
ends, if completely immersed in water and partly 
filled, may be lifted out horizontally and still hold 
the water. A film fills the meshes of the gauze 
and makes the cylinder air-tight; if the film is 
broken by blowing sharply on it, the water will quickly run out. 

37. Capillary Elevation and Depression. — If a line glass 
tube, commonly called a capillary or hairlike tube, is 
partly immersed vertically in water, the water will rise 
higher in the tube than the level outside; on the other 
hand, mercury is depressed below the outside level. The 
top of the little column of water is con¬ 
cave, while that of the column of mercury 
is convex upward (Fig. 27). 

Familiar examples of capillary action are numer¬ 
ous. Blotting paper absorbs ink in its fine pores, 
and oil rises in a wick by capillary action. A 
sponge absorbs water for the same reason; so also 
does a lump of sugar. A cotton or a hemp rope 
absorbs water, increases in diameter, and shortens. 

A liquid may be carried over the top of a vessel 
by capillary action in a large loose cord. Many 
salt solutions construct their own capillary high¬ 
way up over the top of the open glass vessel in which they stand. 
They first rise by capillary action along the surface of the glass, then 
the water evaporates, leaving the salt in fine crystals, through which 
the solution rises still higher by capillary action. This process may 
continue until the liquid flows over the top and down the outside of 
the vessel. 



Figure 27. — 
Concave and 
Convex Surfaces 
in Tubes. 


32 



Figure 26. — 
Contraction of 
Soap Bubble. 















. CAPILLARY ACTION IN SOILS 


33 


38. Laws of Capillary Action. — Support vertically several 
clean glass tubes of small internal diameter in a vessel of pure water 
(Fig. 28). The water will rise in these 
tubes, highest in the one of smallest di¬ 
ameter, and least in the one of greatest. 

With mercury in place of water, the de¬ 
pression will be the greatest in the smallest 
tube. 

If two chemically clean glass plates, in¬ 
clined at a very small angle, be supported 
with their lower edges in water, the height 
to which the water will rise at different 
points will be inversely as the distance be- __ 
tween the plates, and the water line will Figure 2 8. - Capillary 
be curved as in Fig. 29. Elevations. 



These experiments illustrate the following laws : 



Figure 29. — Capillary Elevation 
between Plates. 


I. Liquids ascend in 
tubes when they wet them, 
that is, when the surface 
is concave; and they are 
depressed when they do not 
wet them, that is, when the 
surface is convex . 


II. For tubes of small 
diameter, the elevation or depression is inversely as the 
diameter of the tube. 


39. Capillary Action in Soils. —The distribution of mois¬ 
ture in the soil is greatly affected by capillarity. Water 
spreads through compact porous soil as tea spreads through 
a lump of loaf sugar. As the moisture evaporates at the 
surface, more of it rises by capillary action from the sup¬ 
ply below. To conserve the moisture in dry weather and 
in “ dry farming,” the surface of the soil is loosened by 
cultivation, so that the interstices are too large for free 






























34 


MOLECULAR PHYSICS 


capillary action. The moisture then remains at a lower 
level, where it is needed for the growth of plants. 

40. Capillarity Related to Surface Tension. — The attrac¬ 
tion of water for glass is greater than the attraction of 
water for itself (§ 12). When a liquid is 
thus attracted by a solid, the liquid wets it 
and rises with a concave surface upward 
(Fig. 30). The surface tension in a curved 
film makes the film contract and produces 
c mi a p ressure toward its center of curvature , as 
pgp§||l|fe£g] shown in the case of the soap bubble (§ 36). 

When the surface of the liquid in the tube 
is concave, the result of this pressure toward 
Figure" ^oT— center of curvature is a force upward ; 

Elevation by the downward pressure of the liquid under 
Surface Ten- j s thus reduced, and the liquid rises 

until the weight of the column AE down¬ 
ward just equals the amount of the upward force. When 
the liquid is of a sort like mercury, which does not wet 
the tube, the top of the column is convex, the pressure 
of the film toward its center of curvature is downward, and 
the column sinks until the downward pressure is counter 
balanced by the upward pressure of the liquid outside. 


III. MOLECULAR FORCES IN SOLIDS 

41. Solution of Solids. —The solution of certain solids in 
liquids has become familiar by the use of salt and sugar 
in liquid foods. The solubility of solids is limited, for it 
depends on the nature of both the solid and the solvent,— 
the liquid in which it dissolves. At room temperatures, 
table salt dissolves about three times as freely in water as 
in alcohol; while grease, which is practically insoluble in 
water, dissolves readily in benzine or gasoline. 
























» 






V* 






Common Crystals. 


Quartz (ideal). Quartz (actual). 

Galena or Lead Sulphide. Garnet. 


Alum. 




CR YS TALLIZA TION 


35 


Solution in a small degree takes place in many unsuspected cases. 
Thus, certain kinds of glass dissolve to an appreciable extent in hot 
water. Many rocks are slightly soluble in water, and the familiar 
adage that the “ constant dropping of water wears away a stone ” is 
accounted for, in part at least, by the solution of the stone. Flint 
glass, out of which cut glass vessels are made, dissolves to some extent 
in aqua ammonia; this liquid should not be kept in cut glass bottles, 
nor should cut glass be washed in water containing ammonia. 

There is a definite limit to the quantity of a solid which 
will dissolve at any temperature in a given volume of a 
liquid. For example, 860 g. of table salt will dissolve in 
a liter of water at ordinary temperatures; this is equiva¬ 
lent to three quarters of a pound to the quart. When the 
solution will dissolve no more of the solid, it is said to be 
saturated. As a general rule, though it is not without 
exceptions, the higher the temperature, the larger the 
quantity of a solid dissolved by a liquid. A liquid which 
is saturated at a higher temperature is supersaturated when 
cooled to a lower one. 

42. Crystallization. — When a saturated solution evapo¬ 
rates, the liquid only passes off as a vapor; the dissolved 
substance remains behind as a solid. When the solid 
thus separates slowly from the liquid and the solution 
remains undisturbed, the conditions are favorable for the 
molecules to unite under the influence of their mutual 
attractions, and they assume regular geometric forms 
called crystals . Similar conditions exist when a saturated 
solution cools and becomes supersaturated. The presence 
of a minute crystal of the solid then insures the formation 
of more. The process of the separation of a solid in the 
form of crystals is known as crystallization. 

Dissolve 100 gm. of common alum in a liter of hot water. Hang 
some strings in the solution and set aside in a quiet place for several 
hours. The strings will be covered with beautiful transparent octa- 


36 


MOLECULAR PHYSICS 


hedralcrystals. Copper sulphate may be used in place of the alum; 
large blue crystals will then collect on the strings. 

Filter a saturated solution of common salt and set aside for twen¬ 
ty-four hours. An examination of the surface will reveal groups of 
crystals floating about. Each one of these, when viewed through a 
magnifying glass, will be found to be a little cube. 

Ice is a compact mass of crystals, and snow consists of crystals 
formed from the vapor of water. They are of various forms but all 
hexagonal in outline (Fig. 31 ). 1 



Figure 31. — Snow Crystals. 


43. Elasticity. — Apply pressure to a tennis ball, stretch 
a rubber band, bend a piece of watch spring, twist a strip 
of whalebone. In each case the form or the volume has 
been changed, and the body has been strained. A strain 
means either a change in size or a change in shape. As 
soon as the distorting force, or stress , has been withdrawn, 
these bodies recover their initial shape and dimensions. 
The word stress is applied to the forces acting, while the 
word strain is applied to the effect produced. The property 
of recovery from a strain when the stress is removed is called 
elasticity. It is called elasticity of form when a body re¬ 
covers its form after distortion ; and elasticity of volume 
when the temporary distortion is one of volume. Gases 
and liquids have perfect elasticity of volume, because 

1 These figures were made from microphotographs taken by Mr. W. A. 
Bentley, Jericho, Vermont. 




HOOKE'S LAW 


87 


they recover their former volume when the original pres¬ 
sure is restored. They have no elasticity of form. Some 
solids, such as shoemaker’s wax, lead, putty, and dough, 
when long-continued force is applied, yield slowly and 
never recover. 

The elasticity of a body may be called forth by pressure, 
by stretching, by bending, or by twisting. The bound¬ 
ing ball and the popgun are illustrations of the first ; 
rubber bands are familiar examples of the second ; bows 
and springs of the third ; and the stretched spiral spring 
exemplifies the fourth. 

44. Hooke’s Law. —Solids have a limit to their distor¬ 
tion, called the elastic limit , beyond which they yield and 
are incapable of re¬ 
covering their form 
or volume. The 
elastic limit of steel 
is very high , steel 
breaks before there 
is much permanent 
distortion. On the 



Figure 32.— Bending Proportional to Weight. 


other hand, lead does not recover completely from any 
distortion. 

When the strain in an elastic body does not exceed the 
elastic limit, in general the distortion is proportional to the 
distorting force, or the strain is proportional to the stress „ 
This relation is known as Hooke's law. 


Clamp a meter stick to a suitable support (Fig. 32), and load the 
free end with some convenient weight in a light scale pan; observe 
the bending of the stick by means of the vertical scale and the pointer. 
Then double the weight and note the new deflection. It should be 
double the first. The amount of bending or distortion of the bar is 
proportional to the weight. 








38 


MOLECULAR PHYSICS 


Generally, for all elastic displacements within the 
elastic limit, the distortions of any hind, due to bending, 
stretching, or twisting, are proportional to the forces pro¬ 
ducing them. 

Questions and Exercises 

1. When a glass tube or rod is cut off its edges are sharp. Why 
do they become rounded by softening in a blowpipe flame ? 

2. Why does a small vertical stream of water break into drops? 

3. Why does a dish with a sharp lip pour better than one with¬ 
out it? 

4. A soap bubble is filled, with air. Is the air inside denser or 
rarer than the air outside ? 

5. Explain the action of gasoline in removing grease spots. How 
should it be applied so as to avoid the dark ring which often remains 
after its use ? 

6. The hairs of a camel’s-hair brush separate when placed in water, 
but gather to a point when the brush is removed from the water. 
Explain. 

7. Are the divisions on the scale of a spring balance equal ? 
What law is illustrated ? 

8. In the stone quarries of ancient Egypt it is said that large 
blocks of stone were loosened by drilling a series of holes in the rock, 
driving in wooden plugs, and then thoroughly wetting them. Ex¬ 
plain. 

9. Why is it difficult to write on clean glass with a pen ? 

10. Analysis of the air in a closed room shows little or no difference 
in its composition in different parts of the room. Explain. 

11. If a capillary tube is supported vertically in a vessel of water 
and the tube is shorter than the distance to which water would rise 
in it, will the water flow out of the top ? Why ? 

12. If water rises 15 mm. in a capillary tube of 1.9 mm. diameter, 
what must be the diameter of a tube in which water will rise 45 mm. ? 


CHAPTER III 


MECHANICS OF FLUIDS 
I. PRESSURE OF FLUIDS 

45. Characteristics of Fluids. — A fluid has no shape of 
its own, but takes the shape of the containing vessel, it 
cannot resist a stress unless it is supported on all sides. 
The molecules of a fluid at rest are displaced by the slight¬ 
est force; that is, a fluid yields to the continued applica¬ 
tion of a force tending to change its shape. But fluids 
exhibit wide differences in mobility , or readiness in yield¬ 
ing to a stress. Alcohol, gasoline, and sulphuric ether 
are examples of very mobile liquids; glycerine is very 
much less mobile, and tar still less so. 

In fact, liquids shade off gradually into solids. A stick 
of sealing wax supported at its ends yields continuously 
to its own weight; in warm weather paraffin candles do 
not maintain an upright position in a candlestick, but 
curve over or bend double; a cake of shoemaker’s wax 
on water, with bullets on it and corks under it, yields to 
both and is traversed by them in opposite directions. At 
the same time, sealing wax and shoemaker’s wax when 
cold break readily under the blow of a hammer. 

46. Viscosity. — The resistance of a fluid to flowing under 
stress is called viscosity. It is due to molecular friction. 
The slowness with which a fine precipitate, thrown down 
by chemical action, settles in water is owing to the vis¬ 
cosity of the liquid; and the slow descent of a cloud is 

39 


40 


MECHANICS OF FLUIDS 


accounted for by the viscosity of the air. Viscosity varies 
between wide limits. It is less in gases than in liquids; 
hot water is less viscous than cold water; hence the rela¬ 
tive ease with which a hot solution filters. 



The Mobility of Gasoline Vapor. 


In this six-cylinder automobile engine, gasoline from the tank at the 
right is vaporized in the carburetor at the center. The mobility of the 
vapor is so great that it passes readily through the pipe to the cylinders. 

47. Liquids and Gases. — Fluids are divided into liquids 
and gases. Liquids, such as water and mercury, are but 
slightly compressible, while gases, such as air and hydro¬ 
gen, are highly compressible. A liquid offers great resist¬ 
ance to forces tending to diminish its volume, while a gas 
offers relatively small resistance. Water is reduced only 







pascal's principle 


41 


0.00005 of its Volume by a pressure equal to that of the 
atmosphere (practically 15 lb. to the square inch), while 
air is reduced to one half its volume by the same additional 
pressure. Pressure means force per unit of 
surface. Then, too, gases are distinguished 
from liquids by the fact that any mass of gas 
when introduced into a closed vessel always 
completely fills it, whatever its volume. A 
liquid has a bulk of its own, but a gas has 
not, since a gas expands indefinitely as the 
pressure on it decreases. 

48. Pressure Transmitted by a Fluid. — Fit a 

perforated stopper to an ounce bottle, preferably with Figure 33.— 
flat sides, and mounted in a suitable frame (Fig. 33). Transmission 
Fill the bottle with water and then force a metal ° F ^ RESSURE * 
plunger through the hole in the stopper. If the plunger fits the 
stopper water-tight, the force applied to the 
plunger will be transmitted to the water as a 
bursting force; and the whole force transmitted 
to the inner surface of the bottle will be as many 
times greater than the force applied as the area 
of this surface is greater than that of the end of 
the plunger. 

Figure 34 is a form of syringe made of glass; 
the hollow sphere at the end has several small 
openings. Fill with water and apply force to 
the piston. The water will escape in a series of 
jets of apparently equal velocities, although only 
one of them is directly in line with the piston. 

_ Fit a glass tube to the stem of a small rubber 

Pressure in All ^ a koon; blow into the tube; the balloon will ex- 
Directions. pand equally in all directions, forming a sphere 

and showing equal pressures in all directions. 
A large soap bubble shows the same thing. 

49. Pascal’s Principle. — A solid transmits pressure only 
in the direction in which the force acts; but a fluid trans- 


















42 


MECHANICS OF FLUIDS 


mits pressure in every direction. Hence the law first 
announced by Pascal in 1653 : 

Pressure applied to an inclosed fluid is transmitted 
equally in all directions and without diminution to 
every part of the fluid and of the interior of the contain¬ 
ing vessel. 

This is the fundamental law of the mechanics of fluids. 
It is a direct consequence of their mobility, and it applies 
to both liquids and gases. 

50. The Hydraulic Press. — An important application of 
Pascal’s principle is the hydraulic press. Figure 35 is a 
section showing the principal 
parts. A heavy piston P works 
water-tight in the larger cylin¬ 
der A , while in the smaller one 
the piston p is moved up and 
down as a force pump; it pumps 
water or oil from the reservoir P 
and forces it through the tube C 
into the cylinder A. When the 
piston p of the pump is forced 
down, the liquid transmits the 
pressure to the base of the larger 
piston, on which the force R is as many times the force E 
applied to p as the area of the large piston is greater than 
the area of the small one. If the cross-sectional area of 
the small piston is represented by a, and that of the large 
one by A, the ratio between the forces acting on the two 
pistons is RAP 2 

E a d 2 ' 

where P and d are the diameters of the large and small 
pistons respectively. 



Figure 35. — Hydraulic 
Press. 






















Galileo Galilei (1566— 
1642) was born at Pisa, Italy. 
He was a man of great gen¬ 
ius, and an experimental 
philosopher of the first rank. 
He was educated as a phys¬ 
ician, but devoted his life to 
mathematics and physics. 
He discovered the properties 
of the pendulum, invented 
the telescope bearing his 
name, and was ardent in his 
support of the doctrine that 
the earth revolves around 
the sun. Besides his original 
work in physics, he made interesting discoveries in astronomy. 



Blaise Pascal (1623-1662) 
was born at Clermont in Au¬ 
vergne. He was both a math¬ 
ematician and a physicist. 

Even as a youth he showed 
remarkable learning, and at 
the age of seventeen achieved 
renown with a treatise on 
conic sections. He is best 
known for his announcement 
in 1653 of the important law 
of fluid pressure bearing his 
name. He distinguished him¬ 
self by his researches in conic 
sections, in the properties of 
the cycloid, and the pressure of the atmosphere. 





























APPLICATION OF THE HYDRAULIC PRESS 43 

Thus, if the area A is 100 times the area a, a force of 
10 pounds on the piston p becomes 1000 pounds on P. 
The hydraulic press is a device which permits of the exer¬ 
tion of enormous forces. 

51. Application of the Hydraulic Press.— This machine is 
used in the industries for lifting very heavy weights and 
for compressing materials into small volumes. Instances 
of the former use are the lifting of large crucibles filled 



Figure do . — Commercial Hydraulic Press. 


with molten steel, and of locomotives to replace them on 
the track. The enormous force of the hydraulic press is 
applied also to the baling of cotton and paper, to punching 
holes through steel plates, to making dies, embossing metal, 
and forcing lead through a die in the manufacture of lead 
pipe. A small white pine board one inch thick, compressed 
in an hydraulic press to a thickness of three-eighths inch, 
becomes capable of a high polish and has many of the 
properties of hard wood. 

The commercial press (Fig. 36) is the same in principle 
as Fig. 35, with the addition of some auxiliary parts to 


































44 


MECHANICS OF FLUIDS 


make a working machine. The piston s of the force pump 
may be worked by any convenient power. It has a check 
valve d which closes when s rises and prevents the return 
of the water from the large working cylinder. The piston 
P is surrounded by a peculiar leather collar, without which 
the press is a failure. The larger the pressure in P, the 
closer the leather collar presses against 
the piston and prevents leakage. The 
upper portion of the machine, cut away 
in the figure, differs according to the use 
to which the press is put. 

If the ratio between the cross-sections 
of the two pistons is 500, then when s is 
pressed down with a force of 100 lb. the 
piston P is forced up with a force of 
50,000 lb. 

In the hydraulic press it is evident that 
the small piston travels as many times 
farther than the large one as the force 
exerted by the large piston is greater 
than the effort applied to the small one. 

52. The Hydraulic Elevator. — A mod¬ 
ern application of Pascal’s principle is 
the hydraulic elevator. A simple- form 
is shown in Fig. 37. A long piston P 
carries the cage A, which runs up and 
down between guides and is partly coun¬ 
terbalanced by a weight W. The piston 
Figure 37. — Hy- runs in a tube O sunk in a pit to a depth 
draulic Elevator. e( j Ua j to the height to w hi c h the cage is 

designed to rise. Water under pressure enters the pit 
from the pipe m through the valve v. Turned in one 
direction the valve admits water to the sunken cylinder, 



















DOWNWARD PRESSURE OF A LIQUID 


45 


and the pressure forces the piston up ; when the operator 
turns it in the other direction by pulling a cord, it allows 
the water to escape into the sewer, and the elevator de¬ 
scends by its own weight. 

When greater speed is required, the cage is connected 
to the piston indirectly by a system of pulleys. The cage 
then usually runs four times as fast and four times as far 
as the piston. 

53. Downward Pressure of a Liquid. — Pascal’s principle 
relates to the transmission of pressure applied to a liquid 
in a closed vessel. But a liquid in an open vessel, such 
as water in a bucket, produces pressure because it is 
heavy ; and the pressure of any layer is transmitted to 
every other layer at a lower 
level. Since each layer adds 
its pressure, there must be in¬ 
creasing pressure as the depth 
increases. 

A glass cylinder, B, is cemented into 
a metal ferule, C, which screws into 
a short cylinder, D (Fig. 38). This 
short cylinder is closed at the bottom 
by an elastic diaphragm of thin metal, 
any motion of which caused by water 
in B is communicated by a rack and 
pinion device to the hand on the dial, Figure 38. — Downward Pres- 
E. As the tank, A, filled with water sure Proportional to Depth 
is moved up the supporting rod water flows through the tube, F, 
into the cylinder, B, causing the hand to move over the dial. The 
reading of the hand divided by the depth of the water in B at any 
moment will be practically constant. Hence, 

The downward pressure is proportional to the depth. 

Repeat the experiment with a saturated solution of common salt, 
which is heavier than water. Every pointer reading will be greater 

















46 


MECHANICS OF FLUIDS 


than the corresponding ones with water, but the same relation will 
exist between them. Hence, 

The downward pressure of a liquid 
is proportional to its density (§ 69). 

54. Upward Pressure. — Let a glass 
cylinder A (Fig. 39), such as a straight lamp 
chimney, have its bottom edge ground off so 
as to be closed water tight by a thin piece of 
glass 0. Holding this against the bottom of 
the cylinder by means of a thread C, immerse 
the cylinder in water. The thread may then 
be released and the bottom will stay on be¬ 
cause the water 
presses up against 
it. To release the 
bottom we shall 
have to pour water into the cylinder until the 
levels inside and outside are the same. The 
upward pressure on the bottom of the cylinder 
is then the same as the downward pressure 
inside at the same depth. Or, 

In liquids the pressure upward is 
equal to the pressure downward at 
any depth. 

55 . Pressure at a Point. — The three 
glass tubes of Fig. 40 have short arms of the 
same length, measured from the bend to the 
mouth. They open in different directions, 

— upward, downward, and sidewise. Place 
mercury to the same depth in all the tubes, 
and lower them into a tall jar filled with 
water. When the open ends of the short 
arms are kept at the same level, the change 
in the level of the mercury is the same in all Figure 40. — Pressure 
of them. Hence, Same in All Directions. 

The pressure at a point in a liquid is the same in all 
directions. 




Figure 39. — Upward 
Pressure. 









































TOTAL FORCE ON ANY SURFACE 


47 


The equality of pressure in all directions may also be 
inferred from the absence of currents in a vessel of liquid, 
since an unbalanced pressure would produce motion of 
the liquid. 


56. Bottom Pressure Inde¬ 
pendent of the Shape of the 
Vessel. — Proceeding as in § 53, 
use in succession the three vessels 
shown in Fig. 41. They have equal 
bases, but differ in shape and vol¬ 
ume. They are known as Pascal’s 
vases. Fill each in succession to 
the same height, and note the read¬ 
ing of the pointer. It will be the 
great difference in the amount of w 



Figure 41. — Pressure Independ¬ 
ent of Shape. 


ie for all, notwithstanding the 
. Hence, 


The downward pressure in a liquid is independent of 
the shape of the vessel. 


The apparent contradiction of unequal masses of a 
liquid producing equal pressures is known as the hydro¬ 
static paradox. 

Thus, suppose the circular bottom of a tin pail has an area of 
200 cm. 2 It would be about 16 cm. in diameter. Suppose the pail 
filled with water to a depth of 25 cm. Then the pressure on the 
bottom would be the weight of a prism of water 1 cm. 2 in section 
and 25 cm. high, or 25 g., since a cm. 3 of water weighs one gram. 

The whole force on the bottom would be 200 x 25 = 5000 g., or 
5 kg. If the pail flares, it would contain more than 5000 cm. 8 of 
water and would require more than 5 kg. of force to lift it, but the 
pressure on the bottom would be the same. 

57. Total Force on Any Surface. — It will be seen from 
the example in the last section that the pressure on any 
area is equal to the product of its depth h below the sur¬ 
face of the liquid and the weight d of a unit volume of 
the liquid, or p — hd. If the depth is in centimeters and 









48 


MECHANICS OF FLUIDS 


the weight in grams, the pressure p in water is equal to 
the depth A, since a cubic centimeter of water weighs one 
gram. The pressure, is then in grams per square centi¬ 
meter. But if h is in feet and d in pounds per cubic foot, 
then p = h x 62.4 pounds per square foot, since a cubic 
foot of water weighs 62.4 pounds. To get the pressure 
in pounds per square inch, divide by 144, because there 
are 144 square inches in a square foot. 

The force on any horizontal area A is then 


P = A x h x d . . (Equation 1) 


If the given surface is inclined, then the pressure in¬ 
creases from its value at the highest point submerged to 
its value at the lowest point. In this case h means the 
mean depth of the area, or the depth of its center of figure. 
The total force on any given plane area is always normal, 
that is, perpendicular to it. Equation 1 still applies. 

Examples. To calculate the force on the bottom and sides of a 
cubical box 30 centimeters on each edge, filled with water, and stand¬ 
ing on a horizontal plane: 

The area of each face is 30 x 30 = 900 cm. 2 Then the force on 
the bottom at a depth of 30 cm. is 900 x 30 = 27,000 g. On the sides 


the pressure varies from zero to 
30 g. per square centimeter. The 
average pressure is halfway down 
at a point 15 cm. deep and is 15 
g. per square centimeter. Hence 
the force tending to push out each 
side is 900 x 15 = 13,500 g. 



Figure 42. — Force Against Dam. 


The upstream face of a dam measures 20 ft. from top to bottom, 
but it slopes so that its center of figure is only 7 ft. from the surface 
of the water when the dam is full (Fig. 42). Find the perpendicular 
force against the dam for every foot of length. 

The area of the face of the dam per foot in length is 20 sq. ft. 
Hence the weight of the column of water to represent the force is 
20 x 7 x 62.4 = 8736 lb. 








LEVEL OF LIQUID IN CONNECTED VESSELS 49 



58. Surface of a Liquid at Rest. — The free surface of a 
liquid under the influence of gravity alone is horizontal. 
Even viscous liquids assume a hori¬ 
zontal surface in course of time. 

The sea, or any other large ex¬ 
panse of water, is a part of the 
spheroidal surface of the earth. 

When one looks with a field glass 
at a long straight stretch of the 
Suez Canal near Port Said, the 
water and the retaining wall as 
contrasting bodies appear dis¬ 
tinctly curved as a portion of the 
rounded surface of the earth. Figure 43. —Same Level in 

59. Level of Liquid in Connected All Branches ' 
Vessels. — The water in the apparatus of Fig. 48 rises to 

the same level in all the 
branches. (Why should the 
spout of a teakettle be as high 
as the lid ?) There is equi¬ 
librium because the pressures 
on opposite sides of any cross 
section of the liquid in the 
connecting tube are equal, 
since they are due to liquid 
columns of the same height. 

The glass water gauge , used to 
show the height of the water in a 
steam boiler, is an important appli¬ 
cation of this principle. A thick- 
walled glass tube, AB (Fig. 44), is 
connected at the top with the steam and at the bottom with the water 
in the boiler. The pressure of steam is then the same on the water in 
the boiler and in the gauge tube, and the water level is the same in 



Figure 44. — Water Gauge. 






















50 


MECHANICS OF FLUIDS 


the two. The stopcocks C and D are kept open except when it be¬ 
comes necessary to replace the glass tube. Another stopcock E serves 
to clean out the tube by running steam through it. 

Another application is the water level , consisting of two glass tubes, 
joined by a long rubber tube, and employed by builders for leveling 
foundations. 

60. Artesian Wells. —Artesian or flowing wells illustrate on a 
grand scale the tendency of water to “ seek its level.” In geology an 
artesian basin is one composed of long strata one above the other. 
One of these permits the passage of water, and lies between two layers 
of clay or other material through which water does not pass (Fig. 45). 



Figure 45. —Artesian Well. 


This stratum K crops out at some higher level and here the water 
finds entrance. When a well I is bored through the overlying strata 
in the valley, water issues on account of the pressure transmitted from 
higher points at a distance. There are 8000 or 10,000 artesian wells 
in the western part of the United States; some notable ones are at 
Chicago, St. Louis, New Orleans, Charleston, and Denver. In Europe 
there are very deep flowing wells in Paris (2360 ft.), Berlin (4194 ft.), 
and near Leipzig (5740 ft.). 

61. City Water Supply. — In some cases, where a supply 
of water for city purposes is available at an elevation 
higher than the points of distribution, as in San Francisco, 
Los Angeles, Denver, and New York, the water from the 
source, or from a storage reservoir, is conducted to the city 
in open channels, or in pipes or “ mains,” and the pressure 
causing it to flow is due to gravity alone. Arriving at the 




Elephant Butte Dam. 


Largest mass of masonry in the world. The lake formed by the dam is 
45 miles long and has a capacity four times that of the Assouan Dam 
in Egypt, enough to cover the state of Delaware to a depth of two feet. 




















*• 























































\ 












































































. • • 








CITY WATER SUPPLY 


51 


city, it is distributed through the streets, the pipes ter¬ 
minating at fire hydrants in the streets, and at plugs and 
faucets in buildings. The water is under pressure ade¬ 
quate to carry it to the highest desired points. 

In the absence of a water supply at an elevation, it is 
necessary to pump the water into a reservoir on a high 



point, or into a “ standpipe” or water tower as a part of the 
distributing system. The water rises in the water tower 
to a height corresponding to the pressure maintained by 
the pump. This device serves to equalize the pressure 
throughout the system, and 
in the smaller systems it 
may take the place of a 
reservoir; it may exert 
pressure for domestic pur¬ 
poses and for fire protec¬ 
tion even when the pump 
is not running (Fig. 46). 

For limited domestic supply the hydraulic ram (Fig. 47) is some¬ 
times used. Its action depends on the inertia of a stream of water 
in a pipe. The valve at B is normally open and the other valve open¬ 
ing upward into the air dome is closed. The flow of water through 
the pipe A closes the ball valve B, and the shock of the sudden arrest 
of the flow opens the valve into the air dome ; the water enters to re¬ 
lieve the sudden pressure. Valve B then opens again and the other 
one closes. The flow thus takes place by a succession of pulses. 



Figure 47. — Hydraulic Ram. 

























52 


MECHANICS OF FLUIDS 


Questions and Problems 

1. If a pressure gauge be attached to the water pipe on the top 
floor of a tall building and a second one be attached in the basement, 
will the readings be the same ? Why ? 

2. Why is there danger of bursting a thermos bottle by forcing 
in the stopper when the bottle is full of liquid ? 

3 . In a city supplied with water from a reservoir, to what height 
will the water rise in a vertical pipe connected with the system ? 

4 . Why does a coiled garden hose tend to straighten out when 
the water is turned on ? 

5. Is the pressure against a dam that backs up the water for a 
mile greater than on one that backs up the water for a half mile, 
the depth of water at the dam being the same in both cases ? 

6. The cylinders of a hydraulic press are respectively 6 in. and 
1 in. in diameter. If a force of 100 lb. is applied to the piston of the 
smaller cylinder, what force will the larger piston exert ? 

7 . A tank 10 ft. square and 10 ft. deep, full of water, will exert 
how much force on the bottom ? How much on one side ? 

8. A glass tube 76 cm. long is full of mercury. What is the 
pressure in grams per cm. 2 on the bottom ? (1 cm. 3 of mercury weighs 
13.6 g.) 

9. A glass cylinder 6 in. in diameter and 12 in. deep is full of 
water. What is the force of the water against its cylindrical surface ? 

10. If the pressure gauge of a water system registers 50 lb., how 
high will water rise in a vertical pipe attached thereto ? 

11 . What weight can be supported on the platform of a hydraulic 
elevator, if the piston is 10 in. in diameter and the pressure gauge 
register 50 lb. to the square inch ? 

12. Sea water weighs 64 lb. to the cubic foot. What force will be 
exerted on a board 10 ft. long and 1 ft. wide sunk horizontally in the 
sea to a depth of a mile ? 

13 . The pressure gauge of a water system registers 60 lb. to the 
sq. in. on the ground floor and 30 lb. to the sq. in. on the top floor. 
What is the difference of level ? 

14 . A kerosene tank is 10 ft. in diameter and 10 ft. deep. When 


THE MEASURE OF BUOYANCY 


53 


full of kerosene what force will there be against the cylindrical sur¬ 
face ? (One cubic foot of kerosene weighs 54 lb.) 

15 . A wooden box one foot square has fitted into its top a vertical 
tube 40 ft. long and 1 in. in diameter. When both the tube and box 
are full of water what bursting force is exerted on the inner surface 
of the box ? 

II. BODIES IMMERSED IN LIQUIDS 

62. Buoyancy. — A marble sinks in water and floats in 
mercury; a fresh egg sinks in water and floats in a satu¬ 
rated solution of common salt; a piece of oak floats in 
water and the dense wood lignum-vitae sinks; a swim¬ 
mer in the sea is nearly lifted off his feet by the heavy 
salt water. 

Suspend a pound or two of iron from the hook of a draw scale, 
and note its weight. Now bring a beaker of water up under the iron 
and partly immerse it; note that its weight is diminished; immerse 
farther and the loss of weight increases; after it is fully submerged, 
the loss of weight does not increase with the depth of immersion. 
If salt water is used, the apparent loss of weight will be greater; if 
keroseue, it will be less. In popular language the body immersed is 
said to have lost weight. Its real weight has not changed in the 
least; but an upward force has been brought to bear on it. 

The lifting force of a liquid on a body immersed in it 
is called buoyancy. 

63. The Measure of Buoyancy. — The law of buoyancy 
was discovered by a Greek philosopher Archimedes about 
240 b.c. while engaged in determining the composition 
of the golden crown of Hiero, king of Syracuse, who sus¬ 
pected that the goldsmith had mixed silver with the gold. 
The law is as follows: 

A body immersed in a liquid is buoyed up by a force 
equal to the weight of the liquid displaced by it. 


54 


MECHANICS OF FLUIDS 


The following experiments illustrate the principle of Archimedes, 
which is the basis of the theory of floating bodies: 

The hollow brass cylinder A (Fig. 48) and the 
solid brass cylinder B , which exactly fits into A, are 
suspended from one arm of a balance and carefully 
counterpoised. If now the cylinder A be filled with 
water, the equilibrium will be disturbed; but if at 
the same time cylinder B is immersed in water, as in 
the figure, the equilibrium will be restored. The 
upward force on the solid cylinder is therefore equal 
to the weight of the water in A, and this is equal 
in volume to that of the immersed cylinder. If the 
experiment is tried with any other liquid which 
does not attack brass, the result will be the same. 

A metal cylinder 5.1 cm. long, and 2.5 cm. in di¬ 
ameter has a volume of almost exactly 25 cm. 8 
Suspend it by a fine thread from one arm of a balance 
(Fig. 49) and counterpoise. Then submerge it in 
water as in the figure. The equilibrium will be re¬ 
stored by placing 25 g. in the pan above the cylinder. 
The cylinder displaces 25 cm. 8 of 
water weighing 25 g., and its ap¬ 
parent loss of weight is 25 g. The temperature of 
the water should be near freezing. 


64. Explanation of Archimedes’ Principle. 

— If a cube be immersed, in water (Fig. 
50), the pressures on the vertical sides a 
and b are equal and in opposite direc¬ 
tions. The same is true of the other 
pair of vertical faces. There is therefore 
no resultant horizontal force. On d there 
is a downward force equal to the weight 



Figure 48. — 
Illustrating 
Principle of 
Archimedes. 



Figure 49.— At - 


of the column of water having the face d parent Loss of 


Weight. 


as a base, and the height dn. On c there 
is an upward force equal to the weight of a column of 
water whose base is the area of c, and whose height is cn. 









FLOATING BODIES 


55 



Figure 50. — Explanation of 
Principle. 


The upward force therefore exceeds the downward force 
by the weight of the prism of water whose base is the face 
e of the cube, and whose height is the difference between 
cn and dn , or cd. This is the 
weight of the liquid displaced 
by the cube. 

In general if a cube of any 
material be immersed in water, 
the water pressure at every point 
will be independent of the sub¬ 
stance of the cube. Suppose 
then it is a cube of the water 
itself. Its weight will be a 
vertical force downward. But 
it is in equilibrium, for it does not move. Hence its 
own weight downward is offset by an equal force acting 
vertically upward. But this upward force of the water 
is the same, whatever the material of the cube. Hence, 
there is an upward force on any submerged cube equal 
to the weight of the water displaced by it. A similar 
argument applies to a body of any shape submerged in 
any liquid. 

65. Floating Bodies. If a body be immersed in a 
liquid, it may displace a weight of the liquid less than, 
equal to, or greater than its own weight. In the first 
case, the upward force is less than the weight of the body, 
and the body sinks. In the second case, the upward 
force is equal to the weight of the body, and the body is 
in equilibrium. In the third case, the upward force ex¬ 
ceeds the weight of the body, and the body rises until 
enough of it is out of the liquid so that these forces be¬ 
come equal. The buoyancy is independent of the depth 
so long as the body is wholly immersed, but it decreases 














56 


MECHANICS OF FLUIDS 


as soon as the body begins to emerge from the liquid. 
Hence, 

When a body floats on a liquid it sinks to such a depth 
that the weight of the liquid displaced equals its own 
weight. 

66. Experimental Proof. — Make a wooden bar 20 cm. long and 
1 cm. square (Fig. 51). Drill a hole in one end and fill with enough 
shot to give the bar a vertical position when float¬ 
ing with nearly its whole length in water. Gradu¬ 
ate the bar in millimeters along one edge, beginning 
at the weighted end, and coat with hot paraffin. 
Weigh the bar and float it in water, noting the vol¬ 
ume in cubic centimeters immersed. This volume 
is equal to the volume of water displaced; and 
since 1 cm. 8 of water weighs 1 g., the weight of the 
water displaced is numerically equal to the volume 
of the bar immersed. This will be found also very 
nearly, if not quite, equal to the weight of the 
loaded bar. 

67. The Cartesian Diver. — Descartes, a 
French scientist, illustrated the principle of flota¬ 
tion by means of an hydrostatic 
toy, since called the Cartesian 
diver. It is made of glass, is 

Figure 51. — hollow, and has a small opening 
Experimental near the bottom. The figure is 
Proof - partly filled with water so that 

it just floats in a jar of water (Fig. 52). Pressure 
applied to the sheet rubber tied over the top of the 
jar is transmitted to the water, more water enters 
the floating figure, and the air is compressed. 

The figure then displaces less water and sinks. 

When the pressure is relieved, the air in the diver 
expands and forces water out again. The actual 
displacement of water is then increased, and the Figure 52. — Car- 
figure rises to the surface. The water in the diver tesian Diver. 
may be so nicely adjusted that the little figure will sink in cold 
water, but will rise again when the water has reached the tempera¬ 
ture of the room, and the air in the figure has expanded. 




















THE FLOATING DRY DOCK 


57 



Figure 53.—A United States Submarine. 


A good substitute for the diver is a small inverted homeopathic vial 
in a flat 16-oz. prescription bottle, filled with water and closed with a 
rubber stopper. When pressed, the sides yield, and the vial sinks. 

A submarine boat is a modern Cartesian diver on a large scale. It 
is provided with tight compartments, into which water may be ad¬ 
mitted to make it sink. It may be made to rise to the surface by ex¬ 
pelling some of the water by powerful pumps. 


68. The Floating Dry Dock. — The floating dock re¬ 
sembles the submarine in principle. It is made buoyant 



The Same Submarine Submerging. 








58 


MECHANICS OF FLUIDS 



Figure 54. — Dry Dock. 


by pumping water out of water-tight 
compartments, and by floating it lifts 
a vessel out of the water. In Fig. 54 

A , A are compartments full of air. 
When they are filled with water, 
the dock sinks to the dotted position 

B , B and the vessel is floated into it. 
When the water is pumped out, 
the dock takes the position indi¬ 
cated by the full lines and the vessel 
is lifted out of water. 


III. DENSITY AND SPECIFIC GRAVITY 

69. Density. — We are familiar with the fact that bodies 
of different kinds may have the same size or bulk and yet 
differ greatly in weight, that is, in mass. A block of steel, 
for example, is nearly forty times as heavy as a block of 
cork of the same dimensions, that is, its mass is nearly 
forty times as great. This difference is expressed as a 
difference in density. The density of a substance is the 
number of units of mass of it contained in a unit of volume. 

In the c.g.s. system density is the number of grams per 
cubic centimeter. For example, the density of steel is 7.816 
grams per cubic centimeter (expressed as 7.816 g./cm. 3 ), 
while that of cork has a mean value of about 0.2 g./cm. 3 , 
and that of mercury 13.596 g./cm. 3 So 


or in symbols, 

d — —; whence m = dv, and v = (Equation 2) 

v d 

To illustrate, a slab of marble 20 x 50 x 2 cm. has a volume of 
2000 cm. 8 and weighs 5.4 kg. or 5400 g. Hence its density is 5400/2000 
= 2.7 g./cm. 8 


density = 


volume ’ 
















Floating Dry Dock “Dewey,” now at Manila 










































> 

























DENSITY AND SPECIFIC GRAVITY COMPARED 59 


70. Specific Gravity. — The specific gravity of a body is 
the ratio of its weight to the weight of an equal volume of 
water. If, for example, a cubic inch of lead weighs 11.36 
times as much as a cubic inch of water, the specific gravity 
of lead is 11.36. The principle of Archimedes furnishes 
a simple method of finding specific gravity, since the loss 
of weight of a heavy body suspended in water is equal to 
the weight of the water displaced, or the weight of a vol¬ 
ume of water equal to that of the suspended body. Hence 


specific gravity = 


weight of body 

loss of weight in water 


For example, a piece of copper weighs 880 g. in air and 780 in 
water. Its loss of weight is then 100 g., and this is the weight of the 
water displaced. Hence the specific gravity of copper is 880/100 = 8.8. 


71. Density and Specific Gravity Compared. — Specific 
gravity and density have not quite the same meaning. For 
example, the specific gravity of lead is the abstract num¬ 
ber 11.36, while the density of lead is 11.36 g./cm. 3 , or 
62.4 x 11.36 = 708.9 lb./cu. ft., both of them concrete 
numbers. 

Specific gravity is only a ratio between two masses or 
weights, and is therefore independent of the units em¬ 
ployed in determining it; while density depends on the 
units used to express' it. 

In the c.g.s. system density and specific gravity are 
numerically the same, because the density of water is one 
gram per cubic centimeter, or 

density (g./cm. z ) = specific gravity. 


But in the English system 

density ( lb./cu . ft .) = 62.4 x specific gravity. 



60 


MECHANICS OF FLUIDS 


It is worth remembering that if the density of any sub¬ 
stance is expressed in c. g. s. units, its numerical value is 
always that of the specific gravity. Table IV in the 
Appendix of this book gives the densities in grams per 
cubic centimeter. 

72. Density of Solids. — The density of a solid body is 
its mass divided by its volume. Its mass may always be 
obtained by weighing, but the volume of an irregular solid 
cannot be obtained from a measurement of its dimensions. 
In the c. g. s. system, however, the principle of Archimedes 
furnishes a simple method of finding the volume of a solid, 
however irregular it may be; for in this system the volume 
of an immersed solid is numerically equal to its loss of 
weight in water (§ 63). Then the equa¬ 
tion which defines density (§ 69), 



density = 


mass 

volume 


becomes 

density = 


mass of body 
loss of weight in water 


Figure 55. — 
Solids Heavier 
than Water. 


73. Solids Heavier than Water. — Find 
the mass of the body in air in terms of 
grams; if it is insoluble in water, find 
its apparent loss of. weight by suspending 
it in water (Fig. 55). This loss of 
weight is equal to the weight of the volume of water dis¬ 
placed by the solid (§ 63). But the volume of a body in 
cubic centimeters is the same as the mass in grams of an 
equal volume of water. The mass divided by this volume 
is the density. 

74. Solids Lighter than Water. — If the body floats, its 
volume may still be obtained by tying to it a sinker heavy 










SOLIDS LIGHTER THAN WATER 


61 


enough to force it beneath the surface. Let w 1 denote the 
weight in grams required to counterbalance when the body 
is in the air, and the attached sinker in the water; and 
let w 2 denote the weight to counterbalance when both body 
and sinker are under water (Fig. 56). 

Then obviously w x — w 2 is equal to the 
upward force on the body alone, and is 
therefore numerically equal to the volume 
of the body. The mass divided by this 
volume is the density. 

If the solid is soluble in water, a liquid of 
known density, in which the body is not 
soluble, must be used in place of water. 

Then the loss of weight is equal to the 
weight of the liquid displaced, and if this Figure 56. — 
is divided by the density of the liquid SoLI °s Lighter 
(Equation 2), the volume of the body 
will be obtained. Then the mass of the body divided by 
this volume will be the density sought. 

Examples. — First, for a body heavier than water. 

Weight of body in air.10.5 g. 

Weight of body in water.6.3 g. 

Weight of water displaced.4.2 g. 

Since the density of water is 1 g. per cubic centimeter, the volume 
of the water displaced is 4.2 cm. 3 . This is also the volume of the 
body. Therefore, 10.5 h- 4.2 = 2.5 g. per cubic centimeter is the 
density. 


Second, for a body lighter than water. 

Weight of body in air.4.8 g. 

Weight of sinker in water.10.2 g. 

Weight of body and sinker in water ... 8.4 g. 


The combined weight of the body in air and the sinker in water 
is, then, 4.8 4- 10.2 = 15 g. But when the body is attached to the 








62 


MECHANICS OF FLUIDS 


sinker, their apparent combined weight is only 8.4 g. Therefore 
the buoyant effort on the body is 15 — 8.4 = 6.6 g., and this is the 
weight of the water displaced by the body, and hence its volume is 
6.6 cm. 3 . The density is, then, 4.8 -4- 6.6 = 0.73 g. per cubic centimeter. 

Third, for a body soluble in water. Suppose it is insoluble in alcohol, 
the density of which is 0.8 g. per cubic centimeter. 

Weight of body in air.4.8 g. 

Weight of body in alcohol.3.2 g. 

Weight of alcohol displaced.1.6 g. 

The volume of alcohol displaced is 1.6 -f- 0.8 = 2 cm. 8 . This is 
also .the volume of the body. Therefore, the density of the body is 
4.8 -f- 2 = 2.4 g. per cubic centimeter. 

75. Density of Liquids. — (a) By the specific gravity bottle. 
A specific gravity bottle (Fig. 57) is usually made to hold 
a definite mass of distilled water at a 
specified temperature, for example, 25, 
50, or 100 g. Its volume is therefore 25, 
50, or 100 cm. 3 . To use the bottle, 
weigh it empty, and filled with the liquid, 
the density of which is to be determined. 
The weight of the liquid divided by the 
capacity of the bottle in cubic centimeters 
(the number of grams) is equal to the 
density of the liquid. 

(£>) By the density bulb. 

Specific Gravity The density bulb is a small 
glass globe loaded with shot, 
and having a hook for suspension (Fig. 58). To 
use it, suspend from the arm of a balance with 
a fine platinum wire, and weigh first in air and Figure 58. 
then in water. The apparent loss of weight is ~ Density 
the weight of the water displaced by the bulb. 

Then weigh it again when suspended in the liquid. The 
loss of weight is this time the weight of a volume of the 




Figure 57. — 






DENSITY OF LIQUIDS 


68 


liquid equal to that of the bulb. Divide this loss of weight 
by the loss in water, and the quotient will be the specific 
gravity of the liquid, or its density in 
grams per cubic centimeter (§ 71). 

0?) By the hydrometer. The common 
hydrometer is usually made of glass, and 
consists of a cylindrical stem and a bulb 
weighted with mercury or shot to make it 
sink to the required level (Fig. 59). The 
stem is graduated, or has a scale inside, 
so that readings can be taken at the surface 
of the liquid in which the hydrometer 
floats. These readings give the densities 
directly, or they may be reduced 
to densities by means of an ac¬ 
companying table. Hydrom¬ 
eters sometimes have a ther¬ 
mometer in the stem to indicate 
the temperature of the liquid 
at the time of taking the read- Figure 59.— Hy¬ 
ing. Specially graduated in¬ 
struments of this class are used to test milk, 
alcohol, acids, etc. 

For liquids lighter than water, in which the 
hydrometer sinks to a greater depth, it is cus¬ 
tomary to use a separate instrument to avoid 
so long a stem and scale. 

For testing the acid of a storage battery, the 
— Acid Hy- hydrometer is inclosed in a large glass tube (Fig. 
drometer. go). gy means 0 f the ru bber bulb at the top 
of the large tube enough acid may be drawn in to make the 
hydrometer float. The hydrometer is then read as usual 
and the acid is returned to the cell by squeezing the bulb. 
























64 


MECHANICS OF FLUIDS 


Questions and Problems 

1. Why does an ocean steamer draw more water after entering 
fresh water ? 

2. If the Cartesian diver should sink in the jar, why will the 
addition of salt cause it to rise? 

3. What is the density of a body weighing 15 g. in air and 10 g 
in water? What is its specific gravity? 

4 . A hollow brass ball weighs 1 kg. What must be its volume 
so that it will just float in water? 

5. What is the density of a body weighing 20 g. in air and 16 g. 
in alcohol whose density is 0.8 g. per cubic centimeter? 

6. A bottle filled with water weighed 60 g. and when empty 20 g. 
When filled with olive oil it weighed 56.6 g. What is the density of 
olive oil ? 

7. A density bulb weighed 75 g. in air, 45 g. in water, and 21 g. 
in sulphuric acid. Calculate the density of the sulphuric acid. 

8 . A piece of wood weighs 96 g. in air, 172 g. in water with 
sinker attached. The sinker alone in water weighs 220 g. Find the 
density of the wood. 

9. A piece of zinc weighs 70 g. in air, and 60 g. in water. What 
will it weigh in alcohol of density 0.8 g. per cubic centimeter ? 

10. The mark to which a certain hydrometer weighing 90 g. sinks 
in alcohol is noted. To make it sink to the same mark in water it 
must be weighted with 22.5 g. What is the density of the alcohol ? 

11. A body floats half submerged in water. What is its specific 
gravity? What part of it will be submerged in alcohol, specific 
gravity 0.8? 

12. If an iron ball weighs 100.4 lb. in air, what will it weigh in 
water if its specific gravity is 7.8? 

13. What is the specific gravity of a wooden ball that floats two 
thirds under water ? 

14. A ferry boat weighs 700 tons. What will be the displacement 
of water if it takes on board a train weighing 600 tons ? 

15. A liter flask weighing 75 g. is half filled with water and half 
with glycerine. The flask and liquids weigh 1205 g. What is the 
density of the glycerine? What is its specific gravity? 


PRESSURE PRODUCED BY THE AIR 


65 


IV. PRESSURE OF THE ATMOSPHERE 

76. Weight of Air. — It is only a little more than 250 
years since it became definitely known that air has any 
weight at all. Even now we scarcely appreciate its weight. 

Place a globe holding about a liter (Fig. 61) on the pan of a bal¬ 
ance and counterpoise; the stopcock should be open. Remove the 
globe and force in more air with a bicycle pump, clos¬ 
ing the stopcock to retain the air under the increased 
pressure; the balance will show that the globe is 
heavier than before. Remove it again and exhaust 
the air with an air pump; the balance will now show 
that the globe has lost weight. A large incandescent 
lamp bulb may be used in place of the globe by first 
counterbalancing and then admitting air by punctur¬ 
ing with the very pointed flame of a blowpipe. Thus 
air, though invisible, may be put into a vessel or re- 

° 7 J r nuuKc, 

moved like any other fluid; and, like any other fluid, __ Globe for 
it has weight. Weighing Air. 

The weight of a body of air is surprisingly large. A 
cubic yard of air at atmospheric pressure weighs more 
than 2 lb. The air in a hall 50 ft. long, 30 ft. wide, and 
18 ft. high weighs more than a ton. Precise measure¬ 
ments have shown that air at the temperature of freezing 
and under a pressure equal to that of a column of mer¬ 
cury 76 cm. high weighs 1.293 g. per liter, or 0.001293 g. 
per cubic centimeter. 

77. Pressure Produced by the Air.—Since the air sur¬ 
rounding the earth has weight, it must exert pressure on 
any surface equal to the weight of a column of air above 
it, just as in the case of a liquid. Many experiments 
prove this to be true. We are not aware of this pressure 
because it is equalized in all directions, and we are built 
to sustain it, just as deep-sea fishes sustain the much 
greater pressure of water above them. 




66 


MECHANICS 6F FLUIDS 



Figure 62. — Downward 
Pressure of the Air. 


Stretch a piece of sheet rubber, and tie tightly over the mouth of 
a glass vessel, as shown in Fig. 62. If the air is gradually exhausted 
from the vessel, the rubber will be forced 
down more and more by the pressure of 
the air above it, and it may break. The 
depression will be the same in whatever 
direction the rubber membrane may be 
turned. 

Fill a common tumbler full of water, 
cover with a sheet of paper so as to ex¬ 
clude the air, and holding the hand against 
the paper, invert 
the tumbler (Fig. 

63). When the hand is removed, the paper 
is held against the mouth of the glass with 
sufficient force to keep the water from run¬ 
ning out. 

Cut about 20 cm. from a piece of glass 
tubing of 3 or 4 mm. bore. Dip it vertically 
into a vessel of water, and close the upper 
end with the finger. The tube may now be 
lifted out, and the water will remain in it. 

Figure 64 illustrates a pi¬ 
pette ; it is useful for convey¬ 
ing a small quantity of liquid from one vessel to another. 




Figure 63. - 
Pressure of 


78. The Rise of Liquids in Exhausted Tubes. 

— Near the close of Galileo’s life his patron, 
the Duke of Tuscany, dug a deep well near 
Florence, and was surprised to find that he 
could get no pump in which water would 
rise more than about 32 feet above the level 
in the well. He appealed to Galileo for an 
explanation ; but Galileo appears to have been 
equally surprised, for up to that time every¬ 
body supposed that water rose in tubes exhausted by 
suction because “ nature abhors a vacuum.” Galileo sug- 


Figure 64. 
Pipette. 











Hydro-airplanes. 


When in the air these are sustained by the air-pressure against their 
planes; when on the water, by the water-pressure against their 
pontoons. 







































• 






























I 























pascal's experiments 


67 


gested experiments to find out to what limit nature abhors 
a vacuum, but he was too old and enfeebled in health to 
perform them himself and died before the problem was 
solved by others. 

79. Torricelli’s Experiment. — Torricelli, a friend and 
pupil of Galileo, hit upon the idea of measuring the resist¬ 
ance nature offers to a vacuum by a column of 
mercury in a glass tube instead of a column of 
water in the Duke of Tuscany’s pump. The 
experiment was performed in 1643 by Viviani 
under Torricelli’s direction. 

A stout glass tube about a yard long, sealed 
at one end and filled with clean mercury, is 
closed at the open end with the finger, and in¬ 
verted in a vessel of mercury in a vertical po¬ 
sition (Fig. 65). When the finger is removed, 
the column falls to a height of about 30 inches. 

The space above the mercury is known as a 
Torricellian vacuum. The column of mercury 
in the tube is counterbalanced by the pressure 
of the atmosphere on the mercury in the larger 
vessel at the bottom. 

80. Pascal's Experiments. — To Pascal is due — Torricel- 
the credit of completing the demonstration LI s TuBE ’ 
that the weight of the column of mercury in the Tor¬ 
ricellian experiment measures the pressure of the atmos¬ 
phere. He reasoned that if the mercury is held up 
simply by the pressure of the air, the column should be 
shorter at higher altitudes because there is then less air 
above it. Put to the test by carrying the apparatus to the 
top of the Tour St. Jacques (Fig. 66), 150 feet high, 
at that time the bell tower of a church in Paris, his theory 
was confirmed. A statue of Pascal now stands at the 



Figure 65. 



68 


MECHANICS OF FLUIDS 


base of the old tower. Desiring to carry the test still 
further, he wrote to his brother-in-law to try the experi¬ 
ment on the Puy de Dome, a mountain nearly 1000 m. 
high, in southern France. The result was that the column 

of mercury was found to 
be nearly 8 cm. shorter 
than in Paris. 

Pascal repeated the 
experiment with red 
wine instead of mercury, 
and with glass tubes 
forty-six feet long ; and 
he found that the lighter 
the fluid, the higher the 
column sustained by the 
pressure of the air. 
Further, a balloon, half 
filled with air, appeared 
fully inflated when car¬ 
ried up a high mountain, 
and collapsed again grad¬ 
ually during the descent. 
Thus the question of 
the Duke of Tuscany 
was fully answered; liquids rise in exhausted tubes be¬ 
cause of the pressure of the atmosphere on the surface of 
the liquid outside. 

81. Pressure of One Atmosphere. — The height of the 
column of mercury supported by atmospheric pressure 
varies from hour to hour and with the altitude above the 
sea. Its height is independent of the cross section of the 
tube, but to find the pressure, or force per unit area, a 
tube of unit cross section must be assumed. Suppose an 



Figure 66. — Tour St. Jacques. 





THE BAROMETER 


69 


internal cross-sectional area of 1 cm. 2 . The standard 
height chosen is 76 cm. of mercury at the temperature 
of melting ice (0° C.), and at sea level in lati¬ 
tude 45°. The density of mercury at this tem¬ 
perature is 13.596 grams per cubic centimeter. 

Hence, standard atmospheric pressure , which is 
the weight of this column of mercury, is 

76 x 13.596 = 1033.3 g. per square cen¬ 
timeter, or roughly 1 kg. per square 
centimeter, equivalent to 14.7 
lb. per square inch. 

The height of a column of water to produce 
a pressure of one atmosphere is 76 x 13.596 
= 1033.3 cm. = 33.9 ft. 

82. The Barometer. — The barometer is an 
instrument based on Torricelli’s experiment, 
and is designed to measure the varying pres¬ 
sure of the atmosphere. In its simplest form 
it consists of a J-shaped glass tube about 86 
cm. (34 in.) long, and attached to a support¬ 
ing board (Fig. 67). The short arm has a 
pinhole near the top for the admission of air. 

A scale is fastened by the side of the tube, and 
the difference of readings at the top of the 
mercury in the long arm and the short one gives 
the height of the mercury column sustained by 
atmospheric pressure. This varies from about 
73 to 76.5 cm. for places near sea level. When 
accuracy is required, the barometer reading 
must be corrected for temperature. A good barometer 
must contain pure mercury, and the mercury must be 
boiled in the glass tube to expel air and moisture. 


Figure 67. 
— The Ba¬ 
rometer. 




















70 


MECHANICS OF FLUIDS 


83. The Aneroid Barometer. — A more convenient barom¬ 
eter to carry about is the aneroid barometer, which 
contains no liquid. It consists essentially of a shallow 
cylindrical box (Fig. 68), from which the air is partially 
exhausted. It has a thin cover corrugated in circular 

ridges to give it greater 
flexibility. The cover 
is prevented from col¬ 
lapsing under atmos¬ 
pheric pressure by a 
stiff spring attached to 
the center of the cover 
(shown in the figure 
under the pointer). 
This flexible cover rises 
and falls as the pres¬ 
sure of the atmosphere 
varies, and its motion is 
transmitted to the pointer by means of delicate levers and 
a chain. A scale graduated by comparison with a mer¬ 
curial barometer is fixed under the pointer. These instru¬ 
ments are so sensitive that they readily indicate the change 
of pressure when carried from one floor of a building to 
the next, or even when moved no farther than from a table 
to the floor. 

84. Utility of the Barometer. — The barometer is a faithful 
indicator of all changes in the pressure of the atmosphere. 
These may be due to fluctuations in the atmosphere itself, 
or to changes in the elevation of the observer. 

The barometer is constantly used by the Weather 
Bureau in forecasting changes in the weather. Experi¬ 
ence has shown that barometric readings indicate weather 
changes as follows : 
























CYCLONIC STORMS 


71 


I. A rising barometer indicates the approach of fair 
weather. 

II. A sudden fall of the barometer precedes a storm. 

III. An unchanging high barometer indicates settled fair 
weather. 

The difference in the altitude of two stations may be 
computed from barometer readings taken at the two places 
simultaneously. Various complex rules have been pro¬ 
posed to express the relation between the difference in 
barometer readings and the difference in altitude; a sim¬ 
ple rule for small elevations is to allow 0.1 in. for every 
90 ft. of ascent. 

85. Cyclonic Storms. — Weather maps are drawn from 
observations made at many places at the same time and 
telegraphed to a central 
station. In this way cy- 1 
clonic storms are discov¬ 
ered and followed. At the 
center of the storm is the 
lowest reading of the ba¬ 
rometer. Curves called 
isobars are traced through 
points of equal pressure 
around this center (Fig. 

69). The wind blows from 
areas of higher pressure 
toward those of lower, but 
in the northern hemisphere 
the inflowing winds are de¬ 
flected toward the right on account of the rotation of the 
earth. This gives to the storm a counter-clockwise rota¬ 
tion, as indicated by the arrows in a weather map. Cy- 



Figure 69.— Isobars. 












72 


MECHANICS OF FLUIDS 


clonic storms usually cross the northwest boundary of the 
United States from British Columbia, travel in a south¬ 
easterly direction until they cross the Rocky Mountain 
range, and then turn northeasterly toward the Atlantic 
coast. Storms coming from the Gulf of Mexico usually 
travel along the Atlantic coast toward the northeast. 

Questions and Problems 

1. What are the objections to the use of water as the liquid for 
barometers ? 

2. Why must the air be completely removed from the barometer 
tube? 

3. Why is mercury the best.liquid to use in a barometer tube ? 

4. Point out some of the good points as well as some of the objec¬ 
tionable features of an aneroid barometer. 

5. Must a barometer be suspended out of doors in order to get 
the air pressure ? Why ? 

6. Does the diameter of the bore of a barometer tube affect the 
height to which the mercury rises ? 

7. How can you make water run in a regular stream from a 

8. The barometer reading is 75.2 cm. Calculate the atmospheric 
pressure per square centimeter. 

9. The barometer reading is 29 in. Calculate the atmospheric 
pressure per square inch. 

10. Calculate the buoyancy of the air for a ball 10 cm. in diameter t 
if a liter of air weighs 1.29 g. 

11. The density of glycerine is 1.26 g. per cubic centimeter. If a 
barometer were constructed for glycerine what would be its reading 
when the mercurial barometer reads 73 cm. ? 

12. When the density of the air is 0.0013 g. per cubic centi¬ 
meter, how much less will 200 cm. 3 of cork weigh in air than in a 
vacuum ? 


COMPRESSIBILITY OF AIR 

12 . If a barometer at the foot of a tower reads 29.5 
in., while one at the top reads 29.2 in., what is the height 
of the tower ? 

13. A bottle is fitted air-tight with a rubber stopper 
and a tube as in Fig. 70. If water be sucked out by the 
tube, what will happen when the tube is released? If 

air is blown in through the tube, 
what will happen when the tube is re¬ 
leased ? 

14. Figure 71 represents a pneu¬ 
matic inkstand, nearly full of ink. 

Figure 71. Why does the ink not run out? 

V. COMPRESSION AND EXPANSION OF GASES 

86. Compressibility of Air. — The inflation of a toy bal¬ 
loon, an air cushion, and a pneumatic tire illustrates the 
ready compressibility of the air. 

Push a long test tube under water with its open end 
down. The deeper the tube is sunk, the higher the water 
rises in it and the smaller becomes the volume of the in¬ 
closed air; also the reaction tending to lift the tube in¬ 
creases. 

The expansibility of air, or its tendency to increase in 
volume whenever the pressure is reduced, is shown by its 
escape from any vessel under pressure, such as the rush of 
compressed air from a popgun, an air gun, or a punctured 
pneumatic tire. The air in a building shows the same 
tendency to expahd. When the pressure outside is sud¬ 
denly reduced, as in the passage of a wave due to an ex¬ 
plosion, the force of expansion of the air within often 
bursts the windows outward. 

Blow air into the bottle (Fig. 70) through the open tube. The air 
forced in bubbles up through the water and is compressed within. 
As soon as the tube is released and the pressure in it falls to that of 



73 



Figure 70. 











74 


MECHANICS OF FLUIDS 


Air 

Cushion 





Figure 72.— Air Cushion 
Water Pipe. 


-no 


-100 


the atmosphere, the expansive force of the imprisoned air forces water 
out through the tube with great velocity. This principle is applied in 

many forms of devices for spraying 
plants and shrubbery. 

The compression and the expansion 
of air are both illustrated by the com¬ 
mon pneumatic door check for light 
doors; also by the air dome on a force 
pump; and the air cushion on a water 
pipe (Fig. 72), which is 
usually carried a few 
inches higher than the 
faucet so that the air 
confined in the closed 
end may act as a cushion to take up any sudden shock 
due to the inertia of the water when the stream is sud¬ 
denly checked. The “ pounding ” of the pipes when 
the water is turned off quickly is owing to the absence 
of this air cushion. 

87. Boyle’s Law. — In dealing with air in a 
state of compression or expansion, the question 
at once arises, — how does a given volume of 
air change when the pressure on the air 
changes? The answer is contained in the dis¬ 
covery by Robert Boyle at Oxford, England, 
in 1662. The principle discovered by Boyle 
(and later in France by Mariotte) is known 
as Boyle s law; it applies to all gases at a con¬ 
stant temperature. 

Boyle in his experiments used a J-tube with 
the short arm closed; both arms were pro¬ 
vided with a scale (Fig. 73). In his experi¬ 
ments the pressures extended only from ^ of 
an atmosphere to 4 atmospheres. 

Mercury was poured in until it stood at the same level in both arms 
of the tube. The air in the short arm was then under the same pres- 


—40 


- 


Figure 73. 
— Boyle’s 
Experiment. 





















THE LAW APPROXIMATE 


75 


sure as the atmosphere outside. Its volume was noted by means ot 
the attached scale, and more mercury was then poured into the tube. 
The difference in the level of the mercury in the two arms of the tube 
gave the excess of pressure on the inclosed air above that of the at¬ 
mosphere. When this difference amounted to 76 cm., the pressure on 
the gas in the short tube was 2 atmospheres, and its volume was re¬ 
duced to one half. When the difference became twice 76 cm., the 
pressure on the inclosed air was 3 atmospheres and its volume became 
one third; and so on. 

This is the law of the compressibility of gases; it may 
be expressed as follows : 

At a constant temperature the volume of a given mass 
of gas varies inversely as the pressure sustained by it. 

If the volume of gas v under a pressure p becomes 
volume v l when the pressure is changed to p\ then by the 
law: , 

— P- ; whence pv =p'v' . (Equation 3) 

(Notice the inverse proportion.) In other words, the 
product of the volume of the gas and the corresponding 
pressure remains constant for the same temperature . 

88. The Law Approximate. — Extended investigations 
have shown that Boyle’s law is not rigorously exact for 
any gas. In general, gases are more compressible than 
the law requires, and this is especially true for gases which 
are easily liquefied, such as carbon dioxide (C0 2 ), sulphur 
dioxide (S0 2 ), and chlorine. Within moderate limits of 
pressure, however, Boyle’s law is exceedingly useful in 
dealing with the volume and pressure of gases. 

An example will illustrate its use : If a mass of gas under a pres¬ 
sure of 72 cm. 8 of mercury has a volume of 1900 cm. 3 , what would its 
volume be if the pressure were 76 cm. 8 ? By Equation 3, pv = p'v '; 
hence, 72 x 1900 = 76 x v r . From this equation v f = 1800 cm. 8 . 


76 


MECHANICS OF FLUIDS 


89. The Air Compressor. — A pump designed to compress 
air or other gases under a pressure of several atmospheres 
is shown in section in Fig. 74, and 
complete in Fig. 75. The piston is 
solid, and there are two metal valves 
at the bottom. Air or other gas is 
admitted through the left-hand tube 
when the piston rises; when it de¬ 
scends, it compresses 
the inclosed air, the 
pressure closes the 
left-hand valve, and 
opens the outlet valve on the right, and 
the compressed air is discharged into the 



Figure 74. Section of 
Air Compressor. 


A 


compression tank. 

A bicycle pump (Fig. 76) is an 
air compressor of a very simple 
type. The piston has a cup¬ 
shaped leather collar c , which 
permits the air to pass by into 
the cylinder when the piston is 
withdrawn, but closes when the 
piston is forced in. The collar 
thus serves as a valve, allowing 



Figure 75. — Air 
Compressor. 


the air to flow one way but not the other. The 
compressed air is forced through the tube form¬ 
ing the piston rod, and the check valve in the 
tire inlet prevents its return. 

90. The Air Pump. — The air pump for re¬ 
moving air or any gas from a closed vessel de¬ 
pends for its action on the expansive or elastic 
force of the gas. The first air pump was invented by Otto 
von Guericke, burgomaster of Magdeburg, about 1650. 


Figure 
76. — Bicy¬ 
cle Pump. 
































THE AIR PUMP 


77 



Figure 


77. — Simple 
Pump. 


Air 


In the very simplest form the two valves, corresponding 
with those of the air compressor, are worked by the pressure 
of the air. But though they may 
be made of oiled silk and very 
light, the pressure in the vessel to 
be exhausted soon reaches a lower 
limit below which it is too small 
to open the valve between it and 
the cylinder of the pump. On 
this account automatic valves, 
operated mechanically, are in use 
in the better class of pumps. 

The modern pump in its sim¬ 
plest form is shown in Fig. 77. The two valves are oper¬ 
ated by the pressure of the air; they are of oiled silk so 
as to be as light as possible. When 
the piston descends, valve V in the 
piston opens and V r at the bottom 
of the cylinder closes; the reverse 
is true when the piston ascends. 
The limit of exhaustion is reached 
when the elastic force of the rare¬ 
fied air is not sufficient to open 
the valves. 


Figure 78 shows in section the cylinder 
of an air pump in which the valves are 
automatic. A piston P, with a vaive at 
S, works in a cylindrical barrel, commu¬ 
nicating with the outer air by a valve 
V at its upper end, and with the receiver 
to be exhausted by the horizontal tube at 
the bottom. The valve S' is carried by a 



Figure 78. — Air Pump. 


rod passing through the piston, and fitting tightly enough to be lifted 
when the upstroke begins. The ascent of the rod is almost immediately 






















78 


MECHANICS OF FLUIDS 


arrested by a stop near its upper end, and the piston then slides on 
the rod during the remainder of the upstroke. The open valve S' 

allows the air to flow from the vessel 
to be exhausted into the space below 
the piston. At the end of the upstroke 
the valve S' is closed by the lever 
shown in dotted lines. During the 
downward movement the valve S is 
open, and the inclosed air passes 
through it into the upper part of the 
cylinder. The ascent of the piston 
again closes S ; and as soon as the air 
is sufficiently compressed, it opens the 
valve V and escapes. 

Each complete 
double stroke re¬ 
moves a cylinder full 
of air; but as it be¬ 
comes rarer with 
each stroke, the mass removed each time is less, 

91. Experiments with the Air Pump.— 

1. Expansibility of air. 

(a) Football. Fill a small 1'ubber foot- 



Figure 79. — Football 
Receiver. 




Figure 80. — 
After Air in 
Receiver is Ex¬ 
hausted. 


ball half full of air, and place under a big 
bell jar on the table of the air pump 
(Fig. 79). When the air is exhausted 
from the jar, the football expands until 
it is free from wrinkles (Fig. 80). A toy balloon may 
be substituted. 

( b ) Bolthead. A glass tube with a large bulb blown 
on one end (Fig. 81) is known as a bolthead. The stem 
passes air-tight through the cap of the bell jar, and dips 
below the surface of the water in the inner vessel. When 
the air is exhausted from the jar, the air in the bolthead 
expands and escapes in bubbles through the water. 
Readmission of air into the jar restores the pressure, 
and drives water into the bolthead. Why? 

2. Air pressure, (a) Downward. Wet a piece of parchment paper, 
and tie it tightly over the mouth of a glass cylinder (Fig. 82). A 













EXPERIMENTS WITH THE AIR PUMP 


79 


When 


r\ 




Figure 82. — Bursting 
Parchment Paper. 


sheet of stout paper may be pasted over the cylinder instead, 
the air is exhausted, the paper will break with a loud report. 

(6) The vacuum 
fountain. A tall 
glass vessel has an 
inner jet tube which 
may be closed on the 
outside with a stop¬ 
cock. Exhaust the 
air, place the open¬ 
ing into the jet tube 
in water, and open 
the stopcock. The 
water is forced by 
atmospheric pres¬ 
sure into the exhausted tube like a fountain 
(Fig. 83). 

(c) Upward pressure. A strong glass cyl- 
inder supported on a tripod is fitted with a 
piston (Fig. 84). The brass cover of the 
cylinder is connected with the air pump by 
a thick rubber tube. 

When the air is exhausted, the piston is lifted 
by atmospheric pressure, and carries the heavy 
attached weight. 

(d) The Magdeburg hemispheres. 

This historical piece of apparatus 
w r as designed by Olto von Gue¬ 
ricke to exhibit the great pressure 
of the atmosphere (Fig. 85). The 
lips of the two parts are accurately 
ground to make an air-tight joint 
w r hen greased. When they are 
brought together and the air is 
exhausted, it requires consider- 

Figure 85 a k* e ^ orce to P u ^ them apart. 

— Magde- ^he or i&inal hemispheres of von Guericke were about 22 
burg Hemi- i n * i n diameter, and the atmospheric pressure holding 
spheres. them together was about 5600 lb. 


Figure 83. — Vacuum 
Fountain. 




Figure 84. — Lifting 
Weight by Pressure of 
Atmosphere. 













80 


MECHANICS OF FLUIDS 


92. Buoyancy of the Air. — A small beam balance has 
attached to one arm a hollow closed brass globe; it is 
counterbalanced in air by a solid brass weight on the other 
arm. When the balance is placed under a bell jar, and the 

air is exhausted, the globe overbalances 
the solid weight (Fig. 86). 

The apparatus just described is called 
a baroscope . It shows that the atmos¬ 
phere exerts an upward or buoyant 
force on bodies immersed in it; that is, 
the principle of Archimedes applies to 
gases as well as to liquids. The buoy¬ 
ancy or lifting effect of the atmosphere 
is equal to the weight of the air dis¬ 
placed by a body. Whenever a body is 
FIGU Ba E ro 8 scope THE * ess dense ^ lan weights, it weighs 
more in a vacuum than in the air. 

93. Balloons and airships also illustrate the buoyancy 
of the air. A soap bubble and a toy balloon filled with 
air fall because they are heavier than the air displaced; 
but if filled with hydrogen or coal gas, they rise in the air. 
Their buoyancy is greater than their weight, including 
the inclosed gas. The weight of a balloon with its car 
and contents must be less than that of the air displaced 
by it. The essential part of a balloon is a silk bag, var¬ 
nished to make it air-tight; it is filled either with hydro¬ 
gen or with illuminating gas. A cubic meter of hydrogen 
weighs about 0.09 kg., a cubic meter of illuminating gas, 
0.75 kg., while a cubic meter of air weighs 1.29 kg. 
With hydrogen the buoyancy is 1.29 — 0.09 = 1.2 kg. per 
cubic meter; with illuminating gas it is 1.29 — 0.75 
= 0.54 kg. per cubic meter. The latter is more commonly 
used because it is much cheaper. 





BALLOONS 


81 


A balloon is not fully inflated to start with, but it 
expands as it rises because the pressure of the air on 
the outside diminishes. The buoyancy then decreases 
slowly as the balloon ascends into a rarer atmosphere. If 
it were fully inflated at the start, the inside pressure of 



The British Airship R 34. 

This was the first airship to cross the Atlantic. It is shown here at its 
moorings on Long Island, 


the gas at a high altitude would be greater than the out¬ 
side atmospheric pressure, and the bag would burst. 

Airships are balloons with steering and propelling de¬ 
vices attached. They are made of large volume so as to 
give them considerable lifting force. Huge Zeppelins 
have been made 775 feet long, and holding 32,000 cubic 
feet of gas. They are driven by several gasoline engines 
aggregating from 4000 to 5000 horsepower. Figure 87 













82 


MECHANICS OF FLUIDS 


is a picture of a Zeppelin with the outer rubberized 
cotton cloth D partly cut away, to show the gas balloons 
inside. GG are propellers, shown also in the front view 
in the corner of the picture. The balancing planes and 
the rudder may be seen at the rear end. 



Figure 87.— A Zeppelin. 


Problems and Questions 

1. What limits the height to which a balloon will ascend? 

2. A pound of feathers exactly counterpoises a pound of shot on 
the scale pans of a balance. Do they represent equal masses of mat¬ 
ter ? Explain. 

3. What force will be required to separate a pair of Magdeburg 
hemispheres, assuming the air to be entirely removed from the inside, 
the diameter of the hemispheres being 4 in. and the height of the 
barometer 30 in. ? 

4. The volume of hydrogen collected over mercury in a graduated 
cylinder was 50 cm. 3 , the mercury standing 15 cm. higher in the 
cylinder than outside of it. The reading of the barometer was 75 
cm. How many cubic centimeters of hydrogen would there be at a 
pressure of 76 cm.? 

Suggestion. The height of the mercury in the cylinder above the surface 
of the mercury outside must be subtracted from the barometer reading to get 
the pressure of the gas in the cylinder. 







THE SIPHON 


83 


5 . A test tube is forced down into water with its open end down, 
until the air in it is compressed into the upper half of the tube. 
How deep down is the tube if the barometer stands at 30 in. ? (The 
specific gravity of mercury may be taken as 13.6.) 

6. With what volume of illuminating gas must a balloon be filled 
in order to rise, if the empty balloon and its contents weigh 540 kg. ? 

7 . A mass of iron, density 7.8, weighs 2 kg. in air. How much 
will it weigh in a vacuum ? 

VI. PNEUMATIC APPLIANCES 

94. The Siphon.—The siphon is a U-shaped tube em¬ 
ployed to transfer liquids from one vessel over an inter¬ 
vening elevation to another at a lower 
level by means of atmospheric pressure. 

If the tube is filled and is placed in the 
position shown in Fig. 88, the liquid will 
flow out of the vessel and be discharged 
at the lower level B. 

If the liquid flows outward past the 
highest point of the tube in the direction 
BC , it is because the pressure on the 
liquid outward is greater than the pres¬ 
sure in the other direction. Now the 
outward pressure at the top is the pres¬ 
sure of the atmosphere transmitted by 
the liquid to the top minus the weight FlGUR 5 I p I ^ 0N _ ThE 
of the column of liquid AB ; while the 
pressure inward is the atmospheric pressure transmitted 
to the top by the liquid in BD minus the weight of the 
column BC. Hence, the pressure inward is less than the 
pressure outward by the weight of a column of the liquid 
equal in height to the difference between AB and BC. 

AB and BC are the lengths of the arms of the siphon. 
If the outer arm dips into the liquid in the receiving vessel, 








34 


MECHANICS OF FLUIDS 



the arm terminates at the surface of the liquid. To in¬ 
crease the length CD is to increase the rate of flow. As 
AB and D C approach equality the rate of flow decreases 
and the flow ceases when this difference is zero. The 

siphon fails to work also 
when B is about 33 feet 
above A. Why? 

On a small scale siphons 
are used to empty bottles and 
carboys, which cannot be 
tilted to pour out a liquid; 
also to draw off a liquid 
from a vessel without dis¬ 
turbing the sediment at the 
bottom. 

On a large scale engineers 
have used siphons for drain¬ 
ing lakes and marshes; also 
for lifting water from the 
ocean or other large body of 
water through a pipe leading 
to a steam condenser in a 
power plant, whence it flows 
back through the return pipe 
to the level of the water 
supply. The pipes are con¬ 
tinuous and air-tight, and the 
pump has no work to do ex¬ 
cept to keep the water run¬ 
ning against friction in the 
pipes. There is also a slight back pressure because the water on the 
discharge side is warmer and therefore lighter than on the intake 
side. 

When the mains of a water supply run over hills to a lower level, 
they constitute in reality siphons. Air is carried along with the 
water and collects in the bends at the tops. If there are several of 
these siphons one after another, the back pressure may actually stop 


Siphon Over a Mountain. 

On the far side of the mountain the water 
is lifted by gravity pressure to within 
32 feet of the top. 





THE LIFT PUMP 


85 


the flow of water, unless the air is removed by air 
pumps, or is allowed to escape under pressure through 
relief valves. 

An intermittent siphon (Fig. 89) has its short arm 
inside a vase and its long arm passing through the 
bottom. The vase will hold water until its level 
reaches the top of the bend of the siphon. It then 
discharges and empties the vessel, if it discharges 
faster than it is filled. Again the water rises in the 
vase, and the siphon again emp¬ 
ties it. Intermittent springs are 
supposed to operate on the same 
principle. 

A siphon fountain may be made 
with a Florence flask and glass 
tubing (Fig. 90). The flask is partly filled with 




•Vent Pipe to Roof 


Figure 89.— 
Inter mi ttent 
Siphon. 


water, and the apparatus is then inverted as shown. 
The water enters the flask as a jet. If a piece 
of rubber tubing is attached to the longer arm, the 
jet will rise as the end of the tubing is lowered. 
A portion of the water runs out at first, producing 
a partial vacuum inside. 

A siphon in a vacuum 
made of glass tubing about 
2 mm. in diameter may be 
set up with mercury as the 
liquid. If it is set in action under a tall bell 
jar on the air pump, it will stop working when 
the air is exhausted from the jar, but will be¬ 
gin again when the air is admitted. 

The water in an S -trap, in common use under 
sinks and washbowls, may be siphoned off when 
the discharge pipe is filled with water for a 
short distance below the trap, unless the trap 
is ventilated at the top of the S. Fig. 91 


Figure 90.—Siphon 
Fountain. 



shows the method of ventilating such traps. 


95. The Lift Pump.—The common Fioure 9 ,._ Ventila . 
lift or suction pump acts by the pres- tion of S-trap. 

















86 


MECHANICS OF FLUIDS 


sure of the air; it is, in fact, a simple form of air pump; 
but it was in use 2000 years before the air pump was 
invented. The first few strokes 
serve merely to draw out air from 
the pipe below the valve V (Fig. 
92) ; the pressure of the air on 
the water in the well or cistern 
W.\ then forces it up the pipe 
S, and finally through the valve 
V. After that, when the piston 
descends, the valve V 
closes and checks the 
return of the water, 
and water passes 
through the valve V' 
above the piston. 

The next upstroke 
lifts the water to the 
level of the spout. Since the pressure of the 
air lifts the water to the highest point to which 
the piston ascends, it is obvious that this point 
cannot be more than the limit of about 83 ft. 
above the water in the well. Practically it is 
less on account of leakage through the imper¬ 
fect valves. The priming of a pump by pour¬ 
ing in a little water to start it serves to wet 
the valves and make them air-tight. 

For deep wells the piston rod is lengthened 
and the valves v and v 1 are placed far down j 
the well; the long pump rod serves to lift the Figure 93. 
water from the piston to the spout (Fig. 93). —LiftPump. 

96. The Force Pump. — The force pump (Fig. 94) is 
used to deliver water under pressure, either at a point 
































THE AIR BRAKE 


87 



Figure 94. — Force 
Pump. 


higher than the pump into pipes, as in the fire engine, 
into boilers against steam pressure, or into the cylinder 
of the hydraulic press* 

The air dome D is added to secure 
a continuous flow through the delivery j 
pipe d. Water flows out through v r 
only while the piston is descending; 
without the air dome, therefore, water 
would flow through the pipe d only 
during the downstroke of the piston; 
but the water under pressure from the 
piston enters the dome and compresses 
the air. The elastic force of the air 
drives the water out again as soon 
as v f closes. Thus the flow is practically continuous. 

The pump of a steam fire engine is double acting, that 
is, it forces water out while the piston is moving in either 

direction (Fig. 95); so also are 
pumps for waterworks and 
mines. 

97. The Air Brake. — The well- 

known Westinghouse air brake is oper¬ 
ated by compressed air. In Fig. 96 
P is the train pipe leading to a large 
reservoir at the engine in which an 
air compressor maintains a pressure 
of about 75 lb. per square inch. So 
long as this pressure is applied through 
P, the automatic valve V maintains 
communication between P and an auxiliary reservoir R under each 
car, and at the same time shuts off air from the brake cylinder C. 
But as soon as the pressure in P falls, either by the movement of a 
lever in the engineer’s cab or by the accidental parting of the hose 
coupling k , the valve V cuts off P and connects the reservoir R with 
the cylinder C. The pressure on the piston in C drives it powerfully 



Figure 95. — Fire Engine Pump. 


















































88 


MECHANICS OF FLUIDS 


to the left and sets the brake shoes against the wheels. As soon as 
air from the main reservoir is again admitted to the pipe P, the 

valve V reestablishes com¬ 
munication between P and 
R, and the confined air in 
C escapes. The brakes are 
released by the action of 
the spring S in forcing the 
piston back to the right. 

98. Other Applications 
of the Air Pump and the 
Air Compressor. — The 
air pump and the air com¬ 
pressor are extensively used 

Figure 96. — Air Brake. in industry. Sugar refiners 

employ the air pump to re¬ 
duce the boiling point of the sirup by lowering the pressure on its sur¬ 
face in the evaporating pan; manufacturers of soda water use a com¬ 
pressor to charge the water with carbon dioxide; in pneumatic dispatch 




Figure 97.— Riveting Hammer. 


tubes, now extensively used for carrying small packages, both the air 
pump and the compressor are used, one to exhaust the air from the 
tube in front of the closely fitting carriage, and the other to compress 
air in the tube behind it, so as to propel the carriage with great 
velocity. The air compressor is employed to make a forced draft for 


/ 









































































QUESTIONS AND PROBLEMS 


89 


steam boilers, to ventilate buildings, and to operate machinery in 
places difficult of access, as in mines, where it furnishes fresh air as 
well as power. It is employed also in the pneumatic caisson for 
making excavations and laying foundations under water. The cais 
son is a large heavy air chamber which sinks as the soft earth is 
removed from within. When its bottom is below water level, air is 
forced in under sufficient pressure to prevent the entrance of water. 
Access to it is gained by air-tight locks. 

Compressed air is frequently used for operating railway signals, 
and to control automatic heating and ventilating appliances. Pneu¬ 
matic tools are used for calking seams and joints, for stone cutting, 
chipping iron, and riveting. Figure 97 shows a riveting hammer; 
A is the air pipe, B the trigger for controlling the air, and C the 
hammer. 

The vacuum cleaner is essentially a fan driven by an electric motor. 
The fan pushes the air away from one face and atmospheric pressure 
forces air through the mouthpiece of a tube leading to the fan to fill 
the partial vacuum. This stream of air carries with it the dust of 
the rug or carpet. 


Questions and Problems 

1. What will happen if the tip of an incandescent lamp bulb be 
broken off under water? 

I 

2. How can a tumbler of water be inverted (with the aid of a 
card) without spilling the water? 

3. Explain why the “ priming ” of a dry suction pump restores it 
to working condition. 

4 . What sort of rubber tube must be used to connect a receiver 
to be exhausted by an air pump? 

5. What is the limit of pressure to which a large suction water 
pump can subject the intake pipe? Will the pipe collapse if the 
pump “sucks” hard enough? 

6 . When the barometer stands at 29 in., what is the limiting 
height over which a siphon can carry water ? 

7. A vessel 36 in. deep is filled with mercury; can it be com¬ 
pletely emptied by means of a siphon ? 


90 


NEC HA NICS OF FLUIDS 


8 . A diver works in 35 feet of sea water, specific gravity 1.025 
What pressure must the compression pump supply to counterbalance 
the water pressure ? 

9. When the barometer reading is 73 cm., what is the greatest 
possible length of the short arm of a siphon when used for sulphuric 
acid, density 1.84 g. per cubic centimeter? 

10 . If the pressure against the 8 in. piston of an air brake is 801b. 
per square inch, what is the force driving the piston forward ? 


CHAPTER IV 


MOTION 

I. MOTION IN STRAIGHT LINES 

99. All Motion Relative. — Restand motion are relative 
terms only. A body is at rest when its relative position 
with respect to some point, line, or surface remains un¬ 
changed ; but when that relative position is changing, the 
body is in motion. 

The moving about of a person on a ship is relative to the vessel; 
the movement of the ship across the ocean is relative to the earth’s 
surface; the daily motion of the earth’s surface is relative to its axis 
of rotation ; the motion of the earth as a whole is relative to the sun; 
while the sun itself is drifting with other stars through space. 

100. Types of Motion. — Many familiar motions are irreg¬ 
ular in every way, both as to direction and speed. The 
flight of a bird, the running of a boy at play, and even 
the motion of a man riding a horse, are illustrations. We 
shall study only those motions that can be classified and 
reduced to simple terms. 

The line described by a moving body is its path. When 
this path is straight, like that of a falling body, the motion 
is rectilinear; when it is a curved line, like that of a 
rocket, the motion is curvilinear. 

Then there is also simple harmonic motion , exemplified 
by the to-and-fro swing of a pendulum ; and rotary motion 
about an axis, such as the rotation of the earth on its axis, 
and that of the pulley and armature of a stationary elec- 

91 


92 


MOTION 


trie motor. The motion of a carriage wheel along a level 
road, and that of a ball along the floor of a bowling alley 
combine motion of rotation with rectilinear motion. 

101. Speed or Velocity. — If an automobile runs thirty 
miles in an hour and a half, its average speed is 20 miles 
per hour. Speed or velocity is the rate of motion , that is, 
it is the distance traversed per unit of time. In express¬ 
ing a speed or a velocity the time unit must be given as 



The Twentieth Century Limited at Sixty Miles an Hour. 
The railway train is one of our most familiar examples of motion. 


well as the numerical value. Thus, 60 miles per hour, 
5280 feet per minute, and 26.82 meters per second are all 
expressions for the same speed. 

There is but little distinction between speed and ve¬ 
locity. Both express the rate of motion, but velocity is 
generally used to express the rate of motion in a definite 
direction, while speed is rate of motion without reference 
to direction. 

102. Uniform Motion. — If the motion is over equal dis¬ 
tances in equal and successive units of time, the motion is 
uniform and the velocity is constant. In uniform motion 










ACCELERATION 


93 


the whole distance traversed is found by multiplying the 
speed by the time, or 

distance — speed x time. 

In symbols this is written, $ = v x t ; from which 

8 S 

v — ~ and t = - . . (Equation 4) 

t v 

Example. A railway train runs uniformly covering 660 ft. in 
10 min. Then the speed v = ^ — 66 ft. per minute, or £ mi. per 
hour. The distance s = 66 x 10 = 660 ft. The time t = = 10 min. 

The average speed in variable motion is found in the 
same way as in uniform motion, namely, by dividing the 
space traveled by the time. 

103. Velocity at any Instant. — When the motion is vari¬ 
able, the velocity of a body at any instant is the distance 
it would travel in the next unit of time if at that instant 
its m'otion were to become uniform . 

For example : The velocity of a falling body at any 
moment is the distance it would fall during the following 
second, if the attraction of the earth and the resistance of the 
air were both to he withdrawn. The velocity of a ball as it 
leaves the muzzle of a gun is the distance it would pass 
over in the second following if from that instant it should 
continue to move for a second without any change in speed. 
Actually the motion of the body and the ball for the suc¬ 
ceeding second is variable; the question is, what would be 
the velocity if the motion were invariable ? 

104. Acceleration. — When a train runs a mile a minute 
for several minutes, it moves with uniform velocity; but 
when it is starting or slowing down, it is said to be accel¬ 
erated. If the velocity increases, the acceleration is posi¬ 
tive; if it decreases, it' is negative. A falling body goes 


94 


MOTION 


faster and faster ; it has a positive acceleration. A body 
thrown upward goes more and more slowly; it has a 
negative acceleration. A loaded sled starts from rest at 
the top of a long hill; it gains in velocity as it descends 
the hill; it has a positive acceleration. When it reaches 
the bottom, it loses velocity and is retarded, or has a 
negative acceleration, until it stops. Acceleration is the 
rate of change of speed. 

Acceleration = change in speed per unit time. 

Acceleration is always expressed as so many units of 
speed per unit of time. If, for example, a street car start¬ 
ing from rest gains uniformly in speed, so that at the end 
of ten seconds it has a speed of 10 miles per hour, its ac¬ 
celeration is its gain in speed-per-hour acquired in one 
second, or 1 mile-per-hour per second. 

105. Uniform Acceleration. — If the change in velocity is 
the same from second to second, the motion is uniformly 
accelerated. The best example we have of uniformly ac¬ 
celerated motion is that of a falling body, such as a stone 
or an apple. Neglecting the resistance of the air, its gain 
in velocity is 9.8 m .-per-second for every second it falls. 
Its acceleration is therefore 9.8 m ,-per-second per second; 
in other words, it gains in velocity 9.8 m.-per-second for 
every second of time. This is equivalent to an increase in 
velocity of 588 m. -per-second acquired in a minute of time. 
The unit of time enters tw r ice into every expression for 
acceleration, the first to express the change in velocity, 
and the second to denote the interval during which this 
change takes place. 

If an automobile starts from rest and increases its speed one foot a 
second for a whole minute, its velocity at the end of the minute is 
60 ft. per second. Since it gains in one second a velocity of one foot 


DISTANCE TRAVERSED 


95 


a second, and in one minute a velocity of 60 ft. a second, its accelera¬ 
tion may be expressed either as one foot-per-second per secohd, or as 
60 ft.-per-second per minute. Its velocity is constantly changing; its 
acceleration is constant. 

106. Velocity in Uniformly Accelerated Motion. — Suppose 

a body to move from rest in any given direction with a 
constant acceleration of 5 ft.-per-second per second. Its 
velocity at the end of the first second will be 5 ft. per 
second; at the end of two seconds, 2 x 5 ft.; at the end 
of three seconds, 3 x 5 ft.; and at the end of t seconds, 
£ x 5 ft. per second ; that is, 

final velocity = time x acceleration , 
or in symbols, 

v = ta; whence a = -. . (Equation 5) 

Hence, ^ 

In uniformly accelerated motion the speed acquired\ in 
any given time is proportional to the time. 

107. Distance traversed in Uniformly Accelerated Motion. — 

If we can find the mean or average velocity for any 
period of t seconds, the distance s traversed in t seconds 
may be found precisely as in the case of uniform motion 
(§ 102). For a body starting from rest with an accelera¬ 
tion of 5 feet-per-second per second, for example, its ve¬ 
locity at the end of four seconds is 4 x 5 ft. per second, and 
the average velocity for the four seconds is the mean be¬ 
tween 0 and 4 x 5, or 2 x 5 ft. per second, the velocity at 
the middle of the period. So at the end of t seconds the 
average velocity is ^ta ft. per second. Then we have 

distance = average velocity x time, 


96 


. MOTION 


or in symbols, $ = 1 fa x £ = i a fl # (Equation 6) 

Hence, 

In uniformly accelerated motion the distance traversed 
from rest is proportional to the square of the time. 

108. Uniformly Accelerated Motion Illustrated.—The old¬ 
est method of demonstrating uniformly accelerated motion 

was devised by 
Galileo. It con¬ 
sists of an inclined 
plane two or three 
meters long (Fig. 
98), made of a 
straight board with 
a shallow groove, 

down which a mar- 
Figure 98. — Galileo’s Inclined Plane. .. J . . „ 

ble or a steel ball 

may roll slowly enough to permit the distances to be noted. 
For measuring time, a clock beating seconds, or a metro¬ 
nome, may be used. Assume a metronome as shown in 
the figure adjusted to beat seconds. One end of the board 
should be elevated until the ball will roll from a point near 
the top to the bottom in three seconds. 

Hold the ball in the groove against a straightedge in 
such a way that it may be quickly released at a click of 
the metronome. Find the exact position of the straight¬ 
edge near the top of the plane from which the ball will 
roll to the bottom and strike the block there so that the 
blow will coincide with the third click of the metronome 
after the release of the ball. Measure exactly the dis¬ 
tance between the upper edge of the straightedge and the 
block at the bottom and call it 9 d. Next, since distances 
are proportional to the square of the times, let the straight- 







UNIFORMLY ACCELERATED MOTION 


97 


edge be placed at a distance of 4 c? from the block; the 
ball released at this point should reach the block at the 
second click of the metronome after it starts. Finally, 
start the ball against the straightedge at a distance c? 
from the block; the interval this time should be that of 
one beat of the metronome. 


Tabular Exhibit 


Number of 
Beats, t 


1 

2 

3 

4 


Whole Distance 
Fallen, * 

Distance in Succes¬ 
sive Intervals 

Velocities 
Attained, v 

d 

d 

2 d 

4 d 

3 d 

4 d 

9 d 

5 d 

6 d 

16 d 

Id 

8 d 


The third column is derived by 
subtracting the successive numbers 
of the second. To get the fourth 
column, we notice that if t is one 
second in Equation 6, then s=\a\ 
that is, the distance traversed in 
the first second is one half the accel¬ 
eration. But the acceleration is 
the same as the velocity acquired 
the first second. Hence s = \ v 
and d=\v. Therefore the veloc¬ 
ity at the end of the first second 
on the inclined plane is 2 d. Since 
by Equation 5 the velocities are 
proportional to the time, the suc¬ 
ceeding velocities are 4 c?, 6 c?, etc. 

The numbers in the second 


v-2d - 


3d 


v-id - 


5 d 


v-Qd- 


\d \ 


Ad 


>9 d 


7 d 


v=3d' -*-—— -—J 

Figure 99. — Laws of Fall¬ 
ing Bodies. 


> 1 3d 















98 


MOTION 


column show that the distances traversed are proportional 
to the squares of the time [compare Equation 6]; those 
of column three show that the distances in successive 
seconds are as the odd numbers 1, 3, 5, etc. The results 
are shown graphically in Fig. 99. 

Problems 

Note. For the relation between the circumference of a circle and its 
diameter, see the Mensuration Table in the Appendix. 

1. An aviator drives his aeroplane through the air a distance of 
500 km. in 8 hr. 20 min. What was his average speed per minute? 

2 . The engine drives a boat downstream at the rate of 15 mi. an 
hour, while the current runs 3 ft. a second. How long will it take to 
go 50 mi.? 

3. A man runs a quarter of a mile in 48.4 seconds. At that 
speed, what was his time for 100 yd. ? 

4. If a man can run 100 yd. in 10 sec., what would be his time for 
a mile, if it were possible to maintain the same speed? 

5. A procession 100 yd. long, moving at the rate of 3 mi. an hour, 
passes over a bridge 120 yd. long. How long does it take the proces¬ 
sion to pass entirely over the bridge ? 

6. An express train is running 60 mi. an hour. If the train is 
500 ft. long, how many seconds will it be in passing completely over a 
viaduct 160 ft. in length ? 

7. A locomotive driving wheel is 2 m. in diameter. If it makes 
200 revolutions per minute, what is the speed of the locomotive in 
kilometers per hour, assuming no slipping of the wheel on the track? 

8 . An automobile running at a uniform speed of 25 mi. per hour 
is 10 mi. behind another one on the same highway running 20 mi. per 
hour. How long will it take the former to overtake the latter, and 
how far will each machine have gone during this time? 

9. If the acceleration of a marble rolling down an inclined plane 
is 40 cm.-per-second per second, what will be its velocity after 3 sec. 
from rest ? 

10 . How far will a marble travel down an inclined plane in 3 sec. 
if the acceleration is 40 cm.-per-second per second ? 


DIRECTION OF MOTION ON A CURVE 


99 


11 . A body starts from rest, and moving with uniformly acceler¬ 
ated motion acquires in 10 sec. a velocity of 3600 m. per minute. 
What is the acceleration per-second per second. How far does the 
body go in 10 sec. ? 

12 . What acceleration per-minute per minute does a body have if 
it starts from rest and moves a distance of a mile in 5 min.? What 
will be its velocity at the end of 4 minutes ? 

13 . If a train acquires in 2 min. a velocity of 60 mi. an hour, what 
is its acceleration per-minute per minute, assuming uniformly accel¬ 
erated motion ? 

14 . An electric car starting from rest has uniformly accelerated 
motion for 3 min. At the end of that time its velocity is 27 km. an 
hour. What is its acceleration per-minute per minute ? 

15 . A sled is pushed along smooth ice until it has a velocity of 4 
m. per second. It is then released and goes 100 m. before it stops. 
If its motion is uniformly retarded, what is the retardation in centi- 
meters-per-second per second? 

16 . To acquire a speed of 60 mi. an hour in 10 min., how far would 
an express train have to run, provided it started from rest and its 
motion were uniformly accelerated ? 


II. CURVILINEAR MOTION 

109. Direction of Motion on a Curve. — Curvilinear motion , 
or motion along a curved line, occurs more frequently in 
nature than motion in a straight line. The motion of a 
point on the earth’s surface and about 
its axis is in a circle; the motion of 
the earth in its path around the sun 
is along a curve only approximately 
circular; the motion of a rocket or of 
a stream of water directed obliquely 
upward is along a parabolic curve. 

So also is the motion of a baseball 
when batted high in air. The thrown 
44 curved ball,” too, illustrates curvi¬ 
linear motion. 



Figure 100. —Motion 
Along a Curve. 


100 


MOTION 


When the motion is along a curved line, the direction 
of motion at any point , as at B (Fig. 100), is that of the 
line (7Z>, tangent to the curve at the point. This is the 
same as the direction of the curve at the point. 

110. Uniform Circular Motion. —In uniform circular mo¬ 
tion the velocity of the moving body, measured along the 
circle, is constant. There is then no acceleration in the 
direction in which the body is going at any point. But 
while the velocity remains unchanged in value, it varies in 
direction. If a body is moving with constant velocity in 
a straight line, its acceleration is zero in every direction; 
but if the direction of its motion changes continuously , then 
there is an acceleration at right angles to its path and its 
a 7 ) motion becomes curvilinear. If this ac¬ 
celeration is constant, the motion is uni¬ 
form in a circle. Hence, in uniform 
circular motion there is a constant acceler¬ 
ation directed toward the center of the 
circle. It is called centripetal accelera¬ 
tion. 

Figure 101. — Cen- Uniform circular motion consists of a 

tripetal Accslera- uniform motion in the circumference of 
the circle and a uniformly accelerated 
motion along the radius. If v is the uniform velocity 
around the circle whose radius is r, the value of the cen¬ 
tripetal acceleration is 

D 2 # 

0 =—, .... (Equation T) 



or centripetal acceleration 


square of velocity in circle 

radius of circle 


*Let ABO (Fig. 101) be the circle in which the body revolves, and 
AB the minute portion of the circular path described in a very small 
interval of time t. Denote the length of the arc AB by s. Then, since 








Motion and Force. 


Above : White Star Liner “ Britannic.” 

Below: Part of Boston Elevated Company’s Power Plant. 
























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SIMPLE HARMONIC MOTION 


101 


III. SIMPLE HARMONIC MOTION 

111. Periodic Motion. — The motion of a body is said to 
be periodic when it goes through the same series of move¬ 
ments in successive equal periods of time. It is vibratory 
if it is periodic and reverses its direction of motion at the 
end of each period. The motion of the earth around the 
sun is periodic, but not vibratory. A hammock swinging 
in the wind, the pendulum of a clock, a bowed violin 
string, and the prong of a sounding tuning 
fork illustrate both periodic and vibratory 
motion. 

112. Simple Harmonic Motion. — Suspend a 
ball by a long thread and set it swinging in a hori¬ 
zontal circle (Fig. 102). Place a white screen back 
of the ball and a strong light, such as an arc light or 
a Welsbach 
gas light, at 
a distance of 
twelve or fif¬ 
teen feet in 

front and on a level with the ball. Viewed in a 

darkened room, a shadow of the ball will be seen Figure 102._ Simple 

on the screen, moving to and fro in a straight Harmonic Motion. 
line. This motion is very nearly simple harmonic 

and would be perfectly so if the projection could be made with sun¬ 
light, so that the projecting rays were perpendicular to the screen. 



the motion along the arc is uniform, s = vt. AB is the diagonal of a very 
small parallelogram with sides AD and AE. The latter is the distance 
through which the revolving body is deflected toward the center while 
traversing the very small arc AB. Since the acceleration is constant, 
AE — \ at 2 by Equation 6. The two triangles ABE and ABC are simi¬ 
lar. Hence AB? = AE x AC. Calling the radius of the circle r and 
substituting for AB, AE, and A C their values, v 2 t 2 = \at 2 x 2 r = a£ 2 r. 

Then a =—■ 

r 














102 


MOTION 


Simple harmonic motion is the projection of a uniform cir¬ 
cular motion on a straight line in the plane of the circle. 
All pendular motions of small arc are simple harmonic. 
The name appears to be due to the fact that simple musical 
sounds are caused by bodies vibrating in this manner. 


The graph of a simple harmonic motion is obtained as follows: 
Draw the circle adgk (Fig. 103) representing the path of the ball, and 
the straight line ADG its projection on 
the screen. Divide the circumference into 
any even number of equal parts, as twelve. 
Through the points of division let fall per¬ 
pendiculars on AG, as a A, bB, cC , etc. 
Now as the ball moves along the arc adg, 
its shadow appears to the observer to 
move from A through B, C, etc., to G, 
where it momentarily comes to rest. It 
then starts back toward A, at first slowly, 
but with increasing velocity until it passes 
D. Its velocity then decreases, and at A 
it is again zero, and its motion reverses. 


D 


Figure 103. — Graph Simple 
Harmonic Motion. 


/ 1 \ 
/ 1 \ 

!o 1 

1 - 

i 

1 !§! 

\ 1 i 

\ j 

2 


The radius of the circle, or the distance AD , is the 
amplitude of the vibration. Th e period of the motion is the 
time taken by the ball to go once around the circle ; it is 
the same as the time of a double oscillation of the projected 
motion. The frequency of the vibration is the reciprocal 
of the period. For example, if the period is J a second, 
the frequency is 2, that is, two complete vibrations per 
second. This relation finds frequent illustration in musi¬ 
cal sounds, where pitch depends on the frequency ; in 
light, where frequency determines the color ; and in alter¬ 
nating currents of electricity, where a frequency of 50, for 
example, means that a complete wave is produced every 
fiftieth of a second, and that the current reverses 100 times 
per second. 








PROBLEMS 


103 


Two simple harmonic motions of the same period are 
said to differ in phase when they pass through their 
maximum or minimum velocities at a different time. Thus, 
if one has its maximum velocity at the same instant that 
the other has its minimum, the two motions differ in phase 
by a quarter of a period. 


Problems 

1. At what speed must an automobile be driven to go four times 
around a circular track one mile in diameter in thirty minutes? 

2. The equatorial diameter of the earth is about 8000 miles. 
What is the speed in miles per minute of a point on the equator, 
owing to the earth’s rotation on its axis ? 

3 . A conical pendulum swinging in a circle whose diameter is 50 
cm. makes 5 complete revolutions in 15 seconds. What is the centrip¬ 
etal acceleration of the bob ? 

4 . The radius of the moon’s orbit is 240,000 miles, and the moon 
revolves around the earth in 27 days, 8 hours. What is its centripetal 
acceleration with respect to the earth in feet-per-second per second ? 

5 . A balance wheel on a stationary engine is 10 ft. in diameter and 
makes 100 revolutions per minute. A point on its circumference has 
what centripetal acceleration per-second per second? 

6. The earth’s equatorial radius is 20,926,000 feet, and the period 
of the earth’s rotation on its axis is 23 h., 56 min., 4 sec. Calculate the 
the centripetal acceleration per-second per second at the equator. 


CHAPTER V 



MECHANICS OF SOLIDS 

I. MEASUREMENT OF FORCE 

113. Force. — A preliminary definition of force as a push 
or a pull has already been given. The effects of force in 
producing motion are among our commonest observations. 


A British “Tank” Going into Action. 

The “ tank” exerts enough force to break down trees and walls. 

A brick loosened from a chimney or pushed from a scaffold 
falls by the force of gravity ; a mountain stream rushes 
down by reason of the same force in nature; the leaves of 
a tree rustle in the breeze, the branches sway violently in 
the wind, and their trunks are even twisted off by the 

104 




UNITS OF FORCE 


105 


force of the tornado; powder explodes in a rifle and the 
bullet speeds toward its mark; loud thunder makes the 
earth tremble and vivid lightning rends a tree or shatters 
a flagstaff. From many such familiar facts is derived the 
conception that force is anything that produces motion or 
change of motion in material bodies. It remains now to 
explain how force is measured. 

114. Units of Force. — Two systems of measuring force 
in common use are the gravitational and the absolute. The 
gravitational unit of force is the weight of a standard mass, 
such as the pound of force , the gram of force, or the kilo¬ 
gram of force. A pound of force means one equal to the 
force required to lift the mass of a pound against the down¬ 
ward pull of gravity. The same is true of the metric 
units with the difference in the mass lifted. 

Gravitational units of force are not strictly constant 
because the weight of the same mass varies from point to 
point on the earth's surface, and at different elevations. 
The actual force necessary to lift the mass of a pound at 
the poles of the earth is greater than at the equator; it is 
less on the top of a high mountain than in the neighboring 
valleys, and still less than at the level of the sea. Gravi¬ 
tational units of force are convenient for the common pur¬ 
poses of life and for the work of the engineer, but they are 
not suitable for precise measurements, especially in the 
domain of electricity. 

The so-called “absolute ” unit of force in the c.g.s. system 
is the dyne (from the Greek word meaning force). The 
dyne is the force which imparts to a gram mass an acceler¬ 
ation equal to one centimeter-per-second per second . This 
unit is invariable in value, for it is independent of the vari¬ 
able force of gravitation. It is indispensable in framing 
the definitions of modern electrical and magnetic units. 


106 


MECHANICS OF SOLIDS 


115. Relation between the Gram of Force and the Dyne.— 

The gram of force is the pull of the earth on a mass of one 
gram, definitely at sea level and latitude 45°. Since the 
attraction of the earth in New York imparts to a gram 
mass an acceleration of 980 cm.-per-second per second, 
while the dyne produces an acceleration of only 1 cm.-per- 
second per second, it follows that the gram of force in New 
York is equal to 980 dynes, or the dyne is of the gram 
of force. The pull of gravity on a gram mass in other 
latitudes is not exactly the same as in New York, but for 
the purposes of this book it will be sufficiently accurate to 
say that a gram of force is equal to 980 dynes . It will be 
seen, therefore, that the value of any force expressed 
in dynes is approximately 980 times as great as in grams 
of force. Conversely, to convert dynes into grams 
of force, divide by 980. 

116. How a Force is Measured Mechanically. — The 

simplest device for measuring a force is the spring 
balance (Fig. 104). The common draw scale is a 
spring balance graduated in pounds and fractions 
of a pound. If a weight of 15 lb., for example, 
be hung on the spring and the position of the 
pointer be marked, then any other 15 lb. of force 
will stretch the spring to the same extent in any 
direction. If a man by pulling in any direction 
stretches a spring 8 in., and if a weight of 150 
pounds also stretches the spring 3 in., the force 
exerted by the man is 150 pounds of force. 

The spring balance may be graduated in pounds of force, 
kilograms or grams of force, or in dynes. If correctly 
graduated in dynes, it will give right readings at any 
latitude or elevation. Why are the divisions of the scale 
equal ? 



Figure 
104. — 
Spring 
Balance. 





COMPOSITION OF FORCES 


107 


If a line 1 cm. long stands 


Figure 105.—To Represent 
Foj?ce. 


117. Graphic Representation of a Force. — A force has 
not only magnitude but also direction; in addition, it is 
often necessary to know its point of application. These 
three particulars may be represented by a straight line 
drawn through the point of application of the force in the 
direction in which the force acts, and as many units in 
length as there are units of force, or some multiple or 
submultiple of that number, 
for a force of 15 dynes, a line 
4 cm. long, in the direction 
AB (Fig. 105), will represent 
a force of 60 dynes acting 
in the direction from A to B. Any point on the line AB 
may be used to indicate the point at which the force is 
applied. 

If it is desired to represent graphically the fact that 
two forces act on a body at the same time, for example, 
B 4 kg. of force horizontally and 2 kg. 

of force vertically, two lines are drawn 
from the point of application A (Fig. 
106), one 2 cm. long to the right, and 
the other 1 cm. long toward the top 
of the page. The lines AB and AC 
represent the forces in point of appli¬ 
cation, direction, and magnitude, on a scale of 2 kg. of 
force to the centimeter. 


2 kg 


4 kg 


Figure 
F ORCES 

Angles. 


106. — Two 
at Right 


II. COMPOSITION OF FORCES AND OF VELOCITIES 

118. Composition of Forces. — The resultant of two or 
more forces is a single force which will produce the same 
effect on the motion of a body as the several forces acting 
together. (Note the exception in the case of a couple, 
§ 121.) The process of finding the resultant of two or more 





108 


MECHANICS OF SOLIDS 


forces is known as the composition of forces. It will be con¬ 
venient to consider first the composition of parallel forces, 
and then that of forces acting at an angle. The several 
forces are called components. 

119. The Resultant of Parallel Forces. —Suspend two draw 
scales, A and B (Fig. 107), from a suitable support by cords. Attach 

to them a graduated 
bar and adjust the 
draw scales and the 
attached cords so that 
they are vertical. 
Read the scales, then 
attach the weight W 
and again read the 
scales. Note the dis¬ 
tances CE and ED. 
Correct each draw 
scale reading by sub¬ 
tracting from it the 
reading before the 
weight W was added. 
Compare W with the 
sum of these corrected 
readings, and also the 
ratio of the corrected 
readings of A and B 
to that of ED and EC. 
Change the position of E and repeat the observations. It will be 

found in each case that ^ . Hence the following principle : 

The resultant of two parallel forces in the same direc¬ 
tion is equal to their sum; its point of application 
divides the line joining the points of application of the 
two forces into two parts which are inversely as the 
forces. 

120. Equilibrium. — If two or more forces act on a body 
and no motion results, the forces are said to be in equi - 






















RESULTANT OF TWO FORCES AT AN ANGLE 109 


librium. In Fig. 107 the weight W is equal and opposite 
to the resultant of the two forces measured by the draw 
scales A and B. The three forces A, B , and W are in 
equilibrium. Further, each force is equal and opposite to 
the resultant of the other two and is called their equi - 
librant. The equilibrium of a body does not mean that 
its velocity is zero, but that its acceleration is zero. Rest 
means zero velocity ; equilibrium , zero acceleration. 

121. Parallel Forces in Opposite Directions.—If two par¬ 
allel forces act in opposite directions, their resultant is 
their difference, and it acts in the direction of the larger 
force. In Fig. 107 the resultant of A and W is equal and 
opposite to B. 

When the two parallel forces acting in opposite direc¬ 
tions are equal , they form a couple. The resultant of a 
couple is zero; that is, no single force can be substituted 
for it and produce the same effect. A couple produces 
motion of rotation only, in which all the particles of the 
body to which it is applied rotate in circles about a com¬ 
mon axis. For example, a magnetized sewing needle 
floated on water is acted on by a couple when it is dis¬ 
placed from a north-and-south position. One end of the 
needle is attracted toward the north, and the other toward 
the south, with equal and parallel forces. The effect is 
to rotate the needle about a vertical axis until it returns 
to a north-and-south position. The common auger, as a 
carpenter employs it to bore a hole, illustrates a couple in 
the equal and opposite parallel forces applied by the two 
hands. 

122. The Resultant of Two Forces Acting at an Angle. — 

Tie together three cords at D (Fig. 108) and fasten the three ends to 
the hooks of the draw scales A, B, C. Pass their rings over pegs set 
in a board at such distances apart that the draw scales will all be 


110 


MECHANICS OF SOLIDS 


stretched. Record the readings of the scales, and by means of a 
protractor (see Appendix I) measure the angles formed at D by the 
cords. Draw on a sheet of paper three lines meeting at a point D, 
and forming with one another these angles. Lay off on the three 
lines on some convenient scale, distances to represent the readings of 
the draw scales, DF for A, DE for B, and DC for C. With DF and 
DE as adjacent sides, complete the parallelogram DFGE and draw 
the diagonal DG. DG is the resultant of the forces A and B, and its 




@ 


Figure 108 —Resultant of Two . Forces at an Angle. 

length on the scale chosen will be found equal to that of DC, their 
equilibrant. Here again, each force is equal and opposite to the 
resultant of the other two. 

When two forces act together on a body at an angle, the resultant 
lies between the two ; its position and value may be found by apply¬ 
ing the following principle, known as the parallelogram of forces: 

If two forces are represented by two adjacent sides (DF 
and DE ) of a parallelogram , their resultant is represented 
by the diagonal (D 6r) of the parallelogram drawn through 
their common point of application (i>). 






COMPONENT IN A GIVEN DIRECTION 


111 


When the two forces are equal, their resultant lies mid¬ 
way between them. If the two forces are at right angles 
(Fig. 109) the parallelogram becomes 
a rectangle and the two forces and 
their resultant are represented by the 
three sides of a right triangle, AB , 

BB , AB. The value of the resultant 
in this case may be found by com¬ 
puting the hypotenuse of the triangle. 

For example, if the forces at right angles are 6 kg. of force and 
8 kg. of force, their resultant is 



Figure 109. — Forces 
at Right Angles. 



v/6 2 + 8 2 = 10 kg. of force. 

123. Component of a Force in a Given Direction. — It 

frequently occurs that if a force produces any motion, it 

must be in a direction other 
than that of the force itself. 
For example, suppose the force 
AB (Fig. 110) applied to cause 
Figure 110. —Component in a car to move along the rails 
Given Direction. wm. The £ orc0 evidently 

produces two effects; it tends to move the car along the 
rails, and it increases the pressure on them. The two 
effects are produced by the two forces OB and BB re¬ 
spectively. They are therefore the equivalent of AB. 
The force CB is called the component of AB in the direc¬ 
tion of the rails mw, and BB is the component perpen¬ 
dicular to them. The component of a force in a given 
direction is its effective value in this direction. 

To find the component in a given direction , construct on 
the line representing the force , as the diagonal , a rectangle, 
the sides of which are respectively parallel and perpendicular 
to the direction of the required component; the length of the 








112 


MECHANICS OF SOLIDS 


side parallel to the given direction represents the component 
sought. 

Example. Let a force of 200 lb. be applied to a truck, as AB in 
Fig. 110; and let it act at an angle of 30° with the horizontal. Find 
the horizontal component pushing the truck forward. 

Construct a parallelogram on some convenient scale (Appendix I) 
with the angle ABC equal to 30° and AB representing 200 lb. 
Measure the side CB and obtain by the scale used its equivalent in 
pounds of force. CB may be calculated since A CB is a right triangle. 
Since ABC is an angle of 30°, AC is one half of AB. Then, since 
AC denotes 100 lb. of force, 

CB = Vl^ 2 - AC 2 = V200 2 - 100 2 = 173.2 lb. of force. 

124. Illustrations of the Resolution of a Force. — The kite, 
the sailboat, and the aeroplane are familiar illustrations of the 

resolution of the force of the wind. 

In the case of the kite, the forces 
acting are the weight of the kite AB 
(Fig. Ill), the pull of the string AC, 
and the force of the wind LA. AD 
is the resultant of AB and A C. Re¬ 
solve the force of 
the wind into two 
components, one 
perpendicular to 
HK , the face of 
the kite, and the 
other parallel to 
HK. If HK sets itself at such an angle that the 
component of LA perpendicular to HK coincides 
with AD and is equal to it, the kite will be in equi¬ 
librium ; if it is greater than AD, the kite will move 
upward ; if less, it will descend. 

In the case of the sailboat, the sail is set at such 
an angle that the wind strikes the rear face. In 
Fig. 112 BS represents the sail, and AB the direc¬ 
tion and force of the wind. This force may be re¬ 
solved into two rectangular components, CB and 



Figure 112.— 
Forces on Sail¬ 
boat. 



Figure 111. — Forces Acting on 
Kite. 












COMPOSITION AND RESOLUTION OF VELOCITIES 113 



DB, of which CB represents the intensity of the force that drives the 
boat forward. 

In the case of the aeroplane (Fig. 113), if a large flat surface, 
placed obliquely to the ground, be moved along rapidly, it will be 
lifted upward by the vertical component of the reaction of the air 
against it, equivalent to a wind, just as the kite is lifted. In both the 
monoplane and the biplane, large bent surfaces attached to a strong 
light frame are forced through the air by a rapidly rotating propeller 
driven by a powerful gasoline engine (§ 380). By means of suitable 


Figure 113. — The Frenchman Vedrines and his Monoplane. 

levers under control of the driver, these planes, or certain auxiliary 
planes, can be set at an angle to the stream of air against which they 
are propelled. Then, as with the kite, they rise through the air. 
Vertical planes are attached to the frame to serve as rudders in steer¬ 
ing either to the right or the left. 

125. Composition and Resolution of Velocities. — At the 

Paris exposition in 1900 a continuous moving sidewalk 
carried visitors around the grounds. A person walking 
on this platform had a velocity with respect to the ground 
made up of the velocity of the sidewalk relative to the 
ground and the velocity of the person relative to the mov- 





114 


MECHANICS OF. SOLIDS 


ing walk. The several velocities entering the result are 
the component velocities. Velocities may be combined and 
resolved by the same methods as those applying to forces. 
When several motions are given to a body at the same 
time, its actual motion is a compromise between them, 
and the compromise path is the resultant. 


The following is an example of the composition of two velocities 
at right angles: A boat can be rowed in still water at the rate of 5 
mi. an hour; what will be its actual velocity if it be rowed 5 mi. an 
hour across a stream running 3 mi. an hour ? 

Let AB (Fig. 114) represent in length and direction the velocity of 
5 mi. an hour across the stream, and AC, at right angles to AB, the 
velocity of the current, 3 mi. an hour, both 
on the same scale. Complete the parallelo¬ 
gram ABDC, and draw the diagonal AD 
through the point A common to the two 
component velocities. AD represents the 
actual velocity of the boat; its length on the 
same scale as that of the other lines is 5.83. 
The resultant velocity is therefore 5.83 miles 
an hour in the direction AD. 

When the angle between the components is a right angle, as in the 
present case, the diagonal AD is the hypotenuse of the right triangle 
ABD. Its square is therefore the sum of the squares of 5 and 3, or 



Figure 114.— Boat Run 

NING ACROSS STREAM. 


AD = V5 2 + 3 2 = 5.83. 

When the angle at A is not a right angle, the approximate resultant 
may be found by a graphic process of measurement. 


A velocity, like a force, has both direction and magni¬ 
tude, and a component of it in any given direction may be 
found in precisely the same way as in the case of a force, 
(§ 123). The most common case is the resolution into 
components at right angles to each other. In most cases 
it suffices to find the component in the direction in which 
the attention for the time being is directed. The other one 
at right angles is without effect in this particular direction. 




















PROBLEMS 


115 


Problems 

Note. — Solve graphically the problems involving forces and velocities at 
an angle. Where possible, verify by calculation. Consult Appendix I for 
methods of drawing. 

1. Plot a force of 25 g. on a scale of 4 cm. to the gram. 

2. Represent a force of 50 g. by a straight line on a scale of 
10 cm. to the gram. 

3 . Represent by a figure two forces acting at a common point, 
the forces being 15 g. and 20 g. respectively, and the angle between 
their directions being 60°. 

4 . A body is acted on by. two parallel forces, 20 and 30 lb. respec¬ 
tively. These forces act in the same direction and have their points 
of application 60 in. apart. Find the magnitude of the resultant and 
the distance of its point of application from the less force. 

Suggestion. — Let x be the distance of the point of application of the 
resultant from the force 20. Then 60 — * will be the distance from the 

force 30. Then by Art. 119, . 

5 . A weight of 200 lb. is fastened to the middle of a bar four feet 
long. A boy and a man take hold of the bar to carry it. The boy 
takes hold at one end of the bar. Find where the man must take 
hold so that he will carry two-thirds of the load. 

6 . A horse and a colt are hitched side by side in the usual manner 
to a loaded wagon. A force of 300 lb. will just move the wagon. At 
what point of the double-tree must it be attached to the tongue of 
the wagon so that the colt will pull two pounds to the horse’s three, 
the double-tree being 40 in. long. 

7. A stiff bar firmly fastened at one end sticks out horizontally 
over a cliff for 10 ft., and will just support without breaking a weight 
of 100 lb. at the outer end. How far out on the bar may a weight of 
150 lb. be placed with safety? 

8. Resolve a force of 50 dynes into two parallel forces, with their 
points of application 20 and 30 cm. respectively from the given force. 

9. Two forces, 30 and 40 grams, act on a body at an angle of 60°. 
Find the resultant. 

10. A ball is given an eastward direction by the action of a force 
of 20 dynes. At the same time a force of 30 dynes acts on the ball 



116 


MECHANICS OF SOLIDS 


to give it a northward direction. In what direction does it go, and 
what single force will produce the same effect ? 

11. In towing a boat along a stream two ropes were used, the angle 
between them when taut being 45°. A force of 100 lb. was acting on 
one rope and 150 lb. on the other. What resistance did the boat offer 
to being moved ? 

12. A sailboat is going eastward, the wind is from the northwest, 
and the sail is set at an angle of 30° with the direction of the wind. 
If the wind’s velocity is 12 miles an hour, what is the component 
velocity at right angles to the sail ? 

III. NEWTON’S LAWS OF MOTION 

126. Momentum. — So far we have considered different 
kinds of motion, or how bodies move, without reference to 
the mass moved, and without considering the relation 
between force on the one hand and the moving mass and 
its velocity on the other, or why bodies move. Before 
taking up the laws of motion, which outline the relations 
between force and motion, it is necessary to define two 
terms intimately associated with these laws. The first of 
these is momentum. Momentum is the product of the mass 
and the linear velocity of a moving body. 

Momentum = mass x velocity , or M = mv. (Equation 8) 

In the c.g.s. system, the unit of momentum is the mo¬ 
mentum of a mass of 1 g. moving with a velocity of 1 cm. 
per second. It has no recognized name. In the English 
system, the unit of momentum is the momentum of a mass 
of 1 lb. moving with a velocity of 1 ft. per second. 

127. Impulse. — Suppose a ball of 10 g. mass to be fired 
from a rifle with a velocity of 50,000 cm. per second. Its 
momentum would be 500,000 units. If a truck weighing 
50 kg. moves at the rate of 10 cm. per second, its momen¬ 
tum is also 500,000 units. But the ball has acquired its 


FIRST LAW OF MOTION 


117 


momentum in a fraction of a second, while a minute or 
more may have been spent in giving to the truck the 
same momentum. In some sense the effort required to 
set the ball in motion is the same as that required to 
give the equivalent amount of motion to the truck, be¬ 
cause the momenta of the two are equal. 

This equality is expressed by saying that the impulse is 
the same in the two cases. Since the effect is doubled 
if the value of the force is doubled, or if the time during 
which the force continues to act is doubled, it follows that 
impulse is the product of the force and the time it continues 
to act . In estimating the effect of a force, the time ele¬ 
ment and the magnitude of the force are equally impor¬ 
tant. The term impulse takes both into account. 

128. Newton s Laws of Motion. — The laws of motion, 
formulated by Sir Isaac Newton (1642-1727), are to be 
regarded as physical axioms, incapable of rigorous experi¬ 
mental proof. They must be considered as resting on 
convictions drawn from observation and experiment in 
the domain of physics and astronomy. The results de¬ 
rived from their application have so far been found to be 
invariably true. They form the basis of many of the 
important principles of mechanics. 

129. First Law of Motion. — Every body continues in 
its state of rest or of uniform motion in a straight line, 
unless compelled by applied force to change that state . 

This is known as the law of inertia (§ 9), because it 
asserts that a body persists in a condition of rest or of 
uniform motion, unless it is compelled to change that 
state by the action of an external force. It is further 
true that a body offers resistance to any such change in 


118 


MECHANICS OF SOLIDS 


proportion to its mass. Hence the term mass is now often 
used to denote the measure of a body’s inertia (§ 11). 

From this law is also derived the Newtonian definition 
of force, for the law asserts that force is the sole cause of 
change of motion. 

130. Second Law of Motion. — Change of momentum is 

proportional to the impressed force which produces it, 
and takes place in the direction in which the force acts. 

The second law points out two things: 

First. What the measure is of a force which produces 
change of motion. Maxwell restated the second law in 
modern terms as follows : “ The change of momentum of a 
body is numerically equal to the impulse which produces it , 
and is in the same direction ” ; or in other words, 

momentum (mass x velocity) = impulse (force x time). 
Expressed in symbols, mv=ft. . . . (Equation 9) 



The initial velocity of the mass m before the force f 
acted on it is here assumed to be zerd, and v is the veloc¬ 
ity attained in t seconds. Then the total momentum im¬ 
parted in the time t is mv , and therefore is the rate of 
change of momentum. Force is therefore measured by the 


rate of change of momentum. 


Since v - is the rate of change 


of velocity, or the acceleration a (see Equation 5), we may 
write 


f = ma. . . . (Equation 10) 


THIRD LAW OF MOTION 


119 


We see from this that force may also be measured by the 
product of the mass moved and the acceleration imparted to 
it. Therefore when the mass m is unity, the force is 
numerically equal to the acceleration it produces. Hence 
the definition of the dyne (§ 114). 

Second. This law also points out that the change of 
momentum is always in the direction in which the force acts. 
Hence, when two or more forces act together, each pro¬ 
duces its change of momentum independently of the others 
and in its own direction. This principle lies at the founda¬ 
tion of the method of finding the resultant effect of two 
forces acting on a body in different directions (§ 118). 

On a horizontal shelf about two meters above the floor are placed 
two marbles, one on each side of a straight spring fixed vertically over 
a hole in the shelf. One marble rests 
on the shelf and the other is held over 
the hole between the spring and a 
block fixed to the shelf (Fig. 115). When 
the hammer falls and strikes the spring, it pro¬ 
jects the one marble horizontally and lets the other 
one fall vertically. The two reach the floor at the 
same instant. Both marbles have the same vertical 
acceleration. Figure 115. 

— Illustrating 

131. Third Law of Motion. — To every action Second Law of 
there is always an equal and contrary re- Motion * 
action ; or the mutual actions of two bodies are always 
equal and oppositely directed. 

The essence of this law is that all action between two 
bodies is mutual. Such action is known as a stress and a 
stress is always a two-sided phenomenon, including both 
action and reaction. The third law teaches that these two 
aspects of a stress are always equal and in opposite direc¬ 
tions. The stress in a stretched elastic cord pulls the two 






120 


MECHANICS OF SOLIDS 


bodies to which it is attached equally in opposite directions; 
the stress in a compressed rubber buffer or spring exerts 
an equal push both ways; the former is called a tension 
and the latter a pressure . 

Illustrations. The tension in a rope supporting a weight is a 
stress tending to part it by pulling adjacent portions in opposite 
directions. The same is obviously true if two men pull at the ends of 



American Airplane Squadron in Formation. 
Note the perfect alinement. 


the rope. An ocean steamship is pushed along by the reaction of the 
water against the blades of the propeller. The same is true of an 
aeroplane, only in this case the reaction against the blades is by the 
air, and the blades are longer and revolve much faster than in water 
in order to move enough air to furnish the necessary reaction. When 
a man jumps from a rowboat to the shore, he thrusts the boat back¬ 
wards. An athlete would not make a record standing jump from a 
feather bed or a spring board. When a ball is shot from a gun, the 
gun recoils or “ kicks.” All attraction, such as that between a mag¬ 
net and a piece of iron, is a stress, the magnet attracting the iron and 
the iron the magnet with the same force. 



PROBLEMS 


121 


Practical use is made of reaction to turn the oscillating electric fan 
from side to side so as to blow the air in different directions. A rec¬ 
tangular sheet of brass is bent lengthwise at right angles and is pivoted 
so as to turn 90° about a vertical axis (Fig. 

116). When one half of this bent sheet is ex¬ 
posed to the air current, the reaction sustained 
by the blades of the fan on this side is in part 
balanced by the reaction of the bent sheet; 
but on the opposite half of the fan the reaction 
of the blades is not balanced. Hence the 
whole fan turns about a vertical axis on the 
standard until a lever touches a stop and shifts 
the bent strip so as to expose the other half 
of it to the air current from the opposite half 
of the fan. The fan then reverses its slow 
motion and turns to the other side. 

Since force is measured by the rate at which momentum 
changes, the third law of motion is equivalent to the fol¬ 
lowing: 

In every action between two bodies, the momentum 
gained by the one is equal to that lost by the other, or the 
momenta in opposite directions are the same. 

Problems 

1. What relative velocities will equal impulses impart to the 
masses 5 lb. and 8 lb. respectively ? 

2 . A body of 50 g. is moving with a velocity of 20 cm. per second. 
What is its momentum ? 

3. Find the ratio of the momentum of a body whose mass is 
10 lb., moving with a uniform velocity of 50 ft. per second to that of a 
body whose mass is 25 lb. and whose velocity is 20 ft. per second. 

4 . Two bodies have equal momenta. One has a mass of 2 lb. and 
a velocity of 1500 ft. per second, the other a mass of 100 lb. What is 
the velocity of the second body? 

5. What is the velocity of recoil of a gun whose mass is 5 kg., the 
mass of the ball being 25 g. and its velocity 600 m. per second? 




122 


MECHANICS OF SOLIDS 


6. An unbalanced force of 500 dynes acts for 5 sec. on a mass of 
50 g. What will be the velocity produced ? 

7. A force of 980 dynes acts on a mass of 1 g. What is the 
acceleration ? How far will the body go in 10 sec. ? 

8. A force of 400 dynes acts on a body for 10 sec. What will be 
the momentum at the end of this period? 

9. A body is acted on by a force of 100 dynes for 20 sec. and 
acquires a velocity of 200 cm. per second. What is its mass ? 

10. A force of 10 g. acts for 5 sec. on a body whose mass is 15 g. 
What velocity is imparted ? 

11. What force in grams of force can impart to a mass of 50 g. an 
acceleration of 980 cm.-per-second per second? 

12. A force of 50 g. acts for 5 sec. on a mass of 50 g. How far 
will the body have gone in that time, starting from rest ? 

IV. GRAVITATION 

132. Weight.— The attraction of the earth for all bodies is 
called gravity. The weight of a body is the measure of this' 
attraction. It is a pull on the body and therefore a force. 
It makes a body fall with uniform acceleration called the 
acceleration of gravity and denoted by g. If we represent 
the weight of a body by w and its mass by ra, by Equation 
10, w = mg. From this it appears that the weight of a body 
is proportional to its mass , and that the ratio of the weights 
of two bodies at any place is the same as that of their masses. 
Hence, in the process of weighing with a beam balance, 
the mass of the body weighed is compared with that of a 
standard mass. When a beam balance shows equality of 
weights, it shows also equality of masses. 

133. Direction of Gravity. — The direction in which the 
force of gravity acts at any point is very nearly toward 
the earth’s center. It may be determined by suspending 
a weight by a cord passing through the point. The cord 


LAW OF UNIVERSAL GRAVITATION 


123 


is called a plumb line (Fig. 117), and its direction is a ver¬ 
tical line, A plane or line perpendicular to a plumb line 
is said to be horizontal. Vertical lines drawn 
through neighboring points may be considered 
parallel without sensible error. 

134. Center of Gravity. — In Physics a body is 
thought of as composed of an indefinitely large 
number of parts, each of which is acted on by 
gravity. For bodies of ordinary size, these forces 
of gravity are parallel and proportional to the 
masses of the several small parts. The point of 
application of their resultant is the center of gravity 
of the body. 

If the body is uniform throughout, the position 
of its center of gravity depends on its geometri¬ 
cal figure only. Thus, the center of gravity (1) 
of a straight rod is its middle point; ( 2 ) of a 
circle or ring, its center ; (3) of a sphere or a 
spherical shell, its center ; (4) of a parallelo¬ 
gram, the intersection of its diagonals ; (5) of a 
cylinder or a cylindrical pipe, the middle point of Figure 
its axis. i j 7 . __ 

It is necessary to guard against the idea that P l u m f 
the force of gravity on a body acts at its center of LlNE * 
gravity. Gravity acts on all the particles composing the 
body, but its effect is generally the same as if the resultant, 
that is, the weight of the body, acted at its center of gravity. 
It will be seen from the examples of the ring and the cylin¬ 
drical pipe that the center of gravity may lie entirely out¬ 
side the body. 

135. Law of Universal Gravitation. — It had occurred to 
Galileo and the other early philosophers that the attrac¬ 
tion of gravity extends beyond the earth’s surface, but it 





124 


MECHANICS OF SOLIDS 


remained for Sir Isaac Newton to discover the law of uni¬ 
versal gravitation. He derived this great generalization 
from a study of the planetary motions discovered by Kep* 
ler. The law may be expressed as follows: 

Every portion of matter in the universe attracts every 
other portion, and the stress between them is directly pro¬ 
portional to the product of their masses and inversely 
proportional to the square of the distance between their 
centers of mass. 

For spherical bodies, like the sun, the earth, and the 
planets, the attraction of gravitation is the same as if all 
the matter in them were concentrated at their centers; 
hence, in applying to them the law of gravitation, the 
distance between them is the distance between their cen¬ 
ters. Calculations made to find the centripetal accelera¬ 
tion of the moon in its orbit show that it is attracted to 
the earth with a force which follows the law of universal 
gravitation. 

The law of universal gravitation does not refer in any way to 
weight but to mass. It would be entirely meaningless to speak of the 
weight of the earth, or of the moon, or of the sun, but their masses are 
very definite quantities, the ratios of which are well known in as¬ 
tronomy. Thus the mass of the earth is about 80 times that of 
the moon, and the mass of the sun is about 332,000 times that of the 
earth. The weight of a pound mass at the distance of the moon is 
only the weight of a pound mass at the surface of the earth. 

136. Variation of Weight. — Since the earth is not a 
sphere but is flattened at the poles, it follows from the 
law of gravitation that the acceleration of gravity, and 
the weight of any body, increase in going from the equa¬ 
tor toward either pole. If the earth were a uniform 
sphere and stationary, the value of g would be the same 



Sir Isaac Newton (1642-1727) is celebrated for his discoveries 
in mathematics and physics. He was a Fellow of Trinity Col¬ 
lege, Cambridge. He discovered the binomial theorem in alge¬ 
bra and laid the foundation of the calculus. His greatest work is 
the Principia, a treatise on motion and the laws governing it. His 
greatest discoveries are the laws of gravitation and the composi¬ 
tion of white light. 

From Kepler’s laws of the planetary orbits Newton proved that 
the attraction of the sun on the planets varies inversely as the 
squares of their distances. 

He was also distinguished in public life. He sat in Parliament 
for the University of Cambridge, was at one time Master of the 
Mint, and the reformation of the English coinage was largely his 
work. 








EQUILIBRIUM UNDER GRAVITY 


125 


all over its surface. But the value of g varies from point 
to point on the earth’s surface, even at sea level, both 
because the earth is not a sphere and because it rotates 
on its axis. The centripetal acceleration of a point at 
the equator, owing to the earth’s rotation on its axis, is 
the acceleration of gravity g. Since 289 is the 
square of 17, and the centripetal acceleration varies as 
the square of the velocity (§ 110), it follows that if the 
earth were to rotate in one seventeenth of a day, that is, 
17 times as fast as it now rotates, the apparent value of 
g at the equator would become zero, and bodies there 
would lose all their weight. 

The value of g at the equator is 978.1 and at the poles 
988.1, both in centimeters-per-second per second. At 
New York it is 980.15 centimeters-per-second per second, 
or 32.16 feet-per-second per second. 

137. Equilibrium under Gravity. — When a body rests on 
a horizontal plane, its weight is equal and opposite to the 
reaction of the plane. The vertical line through its cen¬ 
ter of gravity must therefore fall within its base of sup¬ 
port. If this vertical line falls outside the base, the 
weight of the body and the reaction of the plane form a 
couple (§ 121), and the body overturns. 

The three kinds of equilibrium are (1) stable , for any 
displacement which causes the center of gravity to rise; 
(2) unstable , for any displacement which causes the cen¬ 
ter of gravity to fall; (3) neutral, for any displacement 
which does not change the height of the center of gravity. 

Fill a round-bottomed Florence flask one quarter full of shot and 
cover them with melted paraffin to keep them in place (Fig. 118). 
Tip the flask over; after a few oscillations it will return to an up¬ 
right position. Repeat the experiment with a similar empty flask; 
it will not stand up, but will rest in any position on its side and with 


126 


MECHANICS OF SOLIDS 


the top on the table. The loaded flask cannot be tilted over without 
raising its center of gravity; in a vertical position it is therefore 

stable and when tipped over, 
unstable, for it returns to 
a vertical position. For the 
empty flask, its center of grav¬ 
ity is lower when it lies on its 
side than when it is erect. 
Rolling it around does not 
change the height of its center 

Figure 118. -Stability of Flasks. of 8 ravit y and ite equilibrium 

is thus neutral. 

The three funnels of Fig. 119 illustrate the three kinds of equi¬ 
librium on a plane. 

A rocking horse, a rocking 
chair, and a half sphere resting 
on its convex side are examples 
of stable equilibrium. An egg 
lying on its side is in neutral 
equilibrium for rolling and 
stable equilibrium for rocking; 
it is unstable on either end. 

A lead pencil supported on its Figure 119. — Stability of Funnels. 
point is in unstable equilib¬ 
rium. Any such body may become stable by attaching weights to 
it in such a manner as to lower the center of 
gravity below the supporting point (Fig. 120). 

138. Stability. —Stability is the state of 
being firm or stable. The higher the center 
of gravity of a body must be lifted to put 
the body in unstable equilibrium or to 

Figure 120. — overturn it, the greater is its stability. 
Center OF Gravity xhis CO ndition'is met by a relatively large 
base and a low center of gravity. A 
pyramid is a very stable form. On account of the large 
area lying within the four feet of a quadruped, its stability 
is greater than that of a biped. A child is therefore able 











QUESTIONS AND PROBLEMS 


127 


to creep “ on all fours ” before it learns to maintain stable 
equilibrium in walking. A boy on stilts has smaller sta¬ 
bility than on his feet because his support is smaller and 
his center of gravity higher. 

Stability may be well illustrated by means of a brick. It has 
greater stability when lying on its narrow side ( 2 " x 8 ") than when 
standing on end; and on its 


i \ 

i \ 


7^ 


y 


broad side (4" x 8 ") its sta¬ 
bility is still greater. Let Fig. 

121 represent a brick lying on 
its narrow side in A and stand¬ 
ing on end in B. In both caseT 
to overturn it its center of 
gravity c is lifted to the same 
height, but the vertical dis¬ 
tance bd through which the center of gravity must be lifted is greater 
in A than in B. 

A tall chimney or tower has no great stability because its base is 
relatively small and its center of gravity high. A high brick wall 
is able to support a great crushing weight, but its stability is small 
unless it is held by lateral walls and floor beams. 


Figure 121. — Degrees of Stability. 


Questions and Problems 

1 . If one jumps off the top of an empty barrel standing on end, 
why is one likely to get a fall? 

2 . Where is the center of gravity of 
a knife supported as in Fig. 122 ? 

3. Given a triangle cut from a uni¬ 
form sheet of cardboard or thin wood. 
Describe two methods of finding its 
center of gravity. How can you tell 
when the right center has been found ? 

4. Represent a hill by the hypotenuse 
of a right triangle, and a ball on the hill 

by a circle, the circumference of the circle just touching the hypote¬ 
nuse of the triangle. How would you represent the weight of the ball ? 
By resolving this force into two components, find the force that rolls 



Figure 122. 







128 


MECHANICS OF SOLIDS 


the ball down the hill and the force with which the ball presses 
against it. 

5. Which is less likely to “ turn turtle ” in rounding a sharp curve, 
an underslung or an overslung automobile? Why? 

6 . A body weighing 150 lb. on a spring balance on the earth 
would weigh how much on the moon, the radius of the moon being 
\ that of the earth and its mass ? 



Figure 123. — Cathedral of Pisa and Leaning Tower. 


7. If the acceleration of gravity is 32.2 ft.-per-second per second 
on the earth, what must it be oh the sun, the radius of the sun being 
taken as 110 times that of the earth and its mass as 330,000 times? 

8 . With what force will a man weighing 160 lb. press on the floor 
of an elevator when it starts with an acceleration of 4 ft.-per-second 
per second, —first going up, and then going down? 

V. FALLING BODIES 

139. Rate at which Different Bodies Fall. — It is a familiar 

fact that heavy bodies, such as a stone or a piece of iron, 











RESISTANCE OF THE AIR 


129 


fall much faster than such light bodies as feathers, bits of 
paper, and snow crystals. Before the time of Galileo it 
was supposed that different bodies fall with velocities pro¬ 
portional to their weights. This erroneous notion was 
corrected by Galileo by means of his famous experiment 
of dropping various bodies from the top of the leaning 
tower of Pisa (Fig. 123) in the presence of professors and 
students of the university in that city. He showed that 
bodies of different materials fell from the top of the tower 
to the ground, a height of 180 feet, in practically the same 
time; also that light bodies, such as paper, fell with ve¬ 
locities approaching more and more nearly those of heavy 
bodies the more compactly they were rolled together in a 
ball. The slight differences in the velocities observed he 
rightly ascribed to the resistance of the air, 
which is relatively greater for light bodies 
than for heavy compact ones. This inference 
Galileo could not completely verify because 
the air pump had not yet been invented. 

140. Resistance of the Air. — Place a small coin 
and a feather, or a shot and a bit of tissue paper, in 
a glass tube from 4 to 6 feet long. It is closed at one 
end and fitted with a stopcock at the other (Fig. 124). 

Hold the tube in a vertical position and suddenly in¬ 
vert it; the coin or the shot will fall to the bottom 
first. Now exhaust the air as perfectly as possible; 
again invert the tube quickly; the lighter body will 
now fall as fast as the heavier one. This experiment is 
known as the “ Guinea and Feather Tube.” It demon- ^^TiTtube 0 
strates that if the resistance of the air were wholly re¬ 
moved, all bodies at the same place would fall with the same accel¬ 
eration. 

An interesting modification of the experiment is the following: 
Cut a round piece of paper slightly smaller than a cent and drop 
the cent and the paper side by side; the cent will reach the floor 




130 


MECHANICS OF SOLIDS 


first. Then lay the paper on the cent and drop them in that position ; 
the paper will now fall as fast as the cent. Explain. 

The friction of the air against the surface of bodies moving through 
it limits their velocity. A cloud floats, not because it is lighter than 
the atmosphere, for it is actually heavier, but because the surface fric¬ 
tion is so large in comparison with the weight of the minute drops of 
water, that the limiting velocity of fall is very small. 

When a stream of water flows over a high precipice, it is broken 
into fine spray and falls slowly. At the Yosemite Fall (Fig. 125) a 
large stream is broken by the resistance of the air until at the bottom 
of its 1400 foot drop it becomes fine spray. 

141. Laws of Falling Bodies. — Galileo verified the fol¬ 
lowing laws of falling bodies: 

I. The velocity attained, by a falling body is propor¬ 
tional to the time of falling. 

II. The distance fallen is proportional to the square of 
the time of descent. 

III. The acceleration is twice the distance a body falls 
in the first second. 

These laws will be recognized as identical with those 
derived for uniformly accelerated motion, §§ 106 and 107. 
If the inclined plane in Galileo’s experiment be tilted up 
steeper, the effect will be to increase the acceleration down 
the plane ; and if the board be raised to a vertical position, 
the ball will fall freely under gravity and the acceleration 
will become g (§ 136). 

Since the acceleration g is sensibly constant for small 
distances above the earth’s surface, the equations already 
obtained for uniformly accelerated motion may be applied 
directly to falling bodies, by substituting g for a in Equa¬ 
tions 5 and 6. Thus we have 

v = gt, . . . (Equation 11) 
s — 2 9 i2 * ° • (Equation 12) 


and 


LAWS OF FALLING BODIES 


131 



Figure 125. — Yosemite Fall. 



132 


MECHANICS OF SOLIDS 


If in Equation 12 t is one second, s = J g ; or the dis¬ 
tance a body falls from rest in the first second is half the 
acceleration of gravity. A body falls 490 cm. or 16.08 ft. 
the first second; and the velocity attained is 980 cm. or 
32.16 ft. per second. 

142. Projection Upward. —When a body is thrown verti¬ 
cally upward, the acceleration is negative, and it loses 
each second g units of velocity (980 cm. or 32.16 ft.). 
Hence, the time of ascent to the highest point is the time 
taken to bring the body to rest. If the velocity lost is g 
units a second, the time required to lose v units of velocity 
will be the quotient of v by < 7 , or 


time of ascent = 


velocity of projection upward 

acceleration of gravity 


In symbols 



(Equation 13) 


For example, if the velocity of projection upward were 
1470 cm. per second, the time of ascent, neglecting the 
frictional resistance of the air, would be or 1*5 sec¬ 

onds. This is the same as the time of descent again to 
the starting point; hence, the body will return to the start¬ 
ing point with a velocity equal to the velocity of projection but 
in the opposite direction. In this discussion of projection 
upward, the resistance of the air is neglected. 


Problems 

Unless otherwise stated in the problem, g is to be taken as 980 cm.- 
or 32 ft.-per-second per second. 

1. The tower of Pisa is 180 ft. high. In what time would a ball 
dropped from the top reach the ground? With what velocity would 
it strike ? 



CENTRIPETAL AND CENTRIFUGAL FORCE 133 


2 . From what height must a ball fall to acquire a velocity of 
1 km. per second ? 

3. With what velocity in a vertical direction must a shell be fired 
just to reach an aeroplane flying at an elevation of one mile? 

4. A ball is fired vertically with an initial velocity of 500 m. per 
second. Neglecting the resistance of the air, to what height will it 
rise, and in what time will it return to the earth ? 

5. An aeroplane flying westward with a velocity of 60 mi. per 
hour and at an elevation of one mile, dropped a bomb while vertically 
over a cathedral. How far from the cathedral did the bomb strike 
the ground and in which direction ? 

6 . A ball fired horizontally reaches the ground in 4 sec. What 
was the height of the point from which it was fired ? 

7. A cannon ball is fired horizontally from a fort at an elevation 
of 122.5 m. above the neighboring sea. How many seconds before it 
will strike the water ? 

8 . The Washington monument is 555 ft. high. Two balls are 
dropped from its top one second apart. How far apart will the balls 
be when the first one strikes the ground ? 

9. An iron ball was dropped from an aeroplane moving eastward 
at the rate of 45 mi. per hour. It reached the ground 528 ft. east of 
the vertical line through the point from which it was dropped. What 
was the elevation of the aeroplane ? 

10 . A body slides without friction down an inclined plane 300 cm. 
long and 24.5 cm. high. If it moves 40 cm. during the first second, 
what is the computed value of g ? 

VI. CENTRIPETAL AND CENTRIFUGAL FORCE 

143. Definition of Centripetal and Centrifugal Force. — 

Attach a ball to a cord and whirl it around by the hand. 
The ball pulls on the cord, the pull increasing with the 
velocity of the ball. If the ball is replaced by a heavier 
one, with the same velocity the pull is greater. If a longer 
cord is used, the pull is less for the same velocity in the 
circle. 


134 


MECHANICS OF SOLIDS 


The constant pull which deflects the body from a rectilinear 
path and compels it to move in a curvilinear one is the cen¬ 
tripetal force. 

The resistance which a body offers on account of its inertia , 
to deflection from a straight line is the centrifugal force. 
When the motion is uniform and circular, the force is at 
right angles to the path of ithe body around the circle and 
constant. 

These two forces are the'two aspects of the stress in the 
cord (third law of motion), the action of the hand on the 
ball, and the reaction of the ball on the hand. . 

144. Value of Either Force — Tire centripetal acceleration 

v 2 

for uniform circular motion (§ 110) is a — — , where v is 

the uniform velocity in the circle, and r is the radius. 
Further, in § 130 the relation between force and accelera¬ 
tion was found to be as follows: force equals the product 
of the mass and the acceleration imparted to it by the force. 
Hence we have 

centripetal force — mass x centripetal acceleration , 
or f—'TdL. . . . (Equation 14) 

This relation gives the value of either the centripetal 
or the equal centrifugal force in the absolute system of 
measurement, because it is derived from the laws of motion 
and is independent of gravity. In the metric system m 
must be in grams, v in centimeters per second, and r in 
centimeters; / is then in dynes. To obtain / in grams of 
force, divide by 980 (§ 115). In the English system, m 
must be in pounds, v in feet per second, and r in feet; 
dividing by 32.2, the result will' be in pounds of force. 




Centrifugal Force. 


Above : Auto Race on a Circular Raised Track. 

Below: Sled in Swiss Winter Sports being thrown over the embank¬ 
ment by centrifugal force. 













ILLUSTRATIONS OF CENTRIFUGAL FORCE 135 


For example: If a mass of 200 g. is attached to a cord 1 m. long 
and is made to revolve with a velocity of 140 cm. per second, the ten- 

sion ill the cord is 200 x = 39,200 dynes = 39209 = 40 grams of 
force. 100 980 

Again if a body having a mass of 10 lb. 1 oz. move in a circle of 
5 ft. radius with a velocity of 20 ft. per second, then the centripetal 

force is/ = ^ = 25 pounds of force. 

5 x 32.2 

145. Illustrations of Centrifugal Force. — Water adhering to 

the surface of a grindstone leaves the stone as soon as the centrifugal 
force, increasing with the velocity, is greater than the adhesion of the 
water to the stone. Grindstones and flywheels occasionally burst when 
run at too high a speed, the latter when the engine runs away after a 
heavy load is suddenly thrown off. When the centripetal force 
ceases to deflect the body from the tangent to the circle, the body 
flies off along the tangent line. A stone is thrown by whirling it in 
a sling and releasing one of the strings. 

A carriage or an automobile rounding a curve at high speed is sub¬ 
ject to strong centrifugal forces, which act through the tires. The 
centripetal force consists solely of the friction between the tires and 
the ground. If the friction is insuffi¬ 
cient, “skidding” takes place. 

When a spherical vessel containing 
some mercury and water is rapidly 
whirled on its axis (Fig. 126), both the 
mercury and the water rise and form 
separate bands as far as possible from 
the axis of rotation, the mercury out- 

, . Figure 126. — Whirling Liquids. 

Centrifugal machines are used m 

sugar refineries to separate sugar crystals from the sirup, and in dye- 
works and laundries to dry yarn and wet clothes by whirling them 
rapidly in a large cylinder with openings in the side. Honey is ex¬ 
tracted from the comb in a similar way. When light and heavy par¬ 
ticles are whirled together, the heavier ones tend toward the outside. 
New milk is an emulsion of fat and a liquid, and the fat globules are 
lighter than the liquid of the emulsion. Hence, when fresh milk is 
w r hirled in a dairy separator, the cream and the milk form distinct 
layers and collect in separate chambers. 











136 


MECHANICS OF SOLIDS 


VII. THE PENDULUM 

146. Simple Pendulum. — Any body suspended so as to 
swing about a horizontal axis is a pendulum. A simple 
pendulum is an ideal one. It may be defined as a material 
particle without size suspended by a cord without weight. 
A small lead ball suspended by a long thread without sen¬ 
sible mass represents very nearly a simple pendulum. 
When at rest the thread hangs vertically like a plumb 
line; but if the ball be drawn aside and released, it will 
oscillate about its position of rest. Its oscillations become 
gradually smaller; but if the arc described be small, the 
period of its swing will remain unchanged. 

This feature of pendular motion first attracted the 
attention of Galileo while watching the slow oscillations of 
a “lamp” or bronze chandelier, suspended by a long rope 
from the roof of the cathedral in Pisa. Galileo noticed 
the even time of the oscillations as the 
path of the swinging chandelier became 
shorter and shorter. Such a motion, 
which repeats itself over and over in 
equal time intervals, is said to b q periodic. 

147. The Motion of a Pendulum. — AN in 

Fig. 127 is a nearly simple pendulum with the 
ball at N. When the ball is drawn aside to the 
position B, its weight, represented by BG, may be 
resolved into two components, BD. in the direc¬ 
tion of the thread, and BC at right angles to it 
and tangent to the arc BNE. The latter is the 
force which produces motion of the ball toward N. 

As the ball moves from B toward N the component BC becomes 
smaller and smaller and vanishes at N , where the whole weight of the 
ball is in the direction of the thread. In falling from B to N, the 
ball moves in the arc of a circle under the influence of a force which 
is greatest at B and becomes zero at N. The motion is therefore 



Figure 127. — 
Forces Acting on a 

PoMTmr 




THE MOTION OF A PENDULUM 


137 



Interior of Pisa Cathedral. 

The bronze chandelier which Galileo observed hangs just in front of the 

altar. 










138 


MECHANICS OF SOLIDS 


accelerated all the way from B to N, but not uniformly. The velocity 
increases continuously from B to N, but at a decreasing rate. 

The ball passes N with its greatest velocity and continues bn toward 
E. From N to E the component of the weight along the tangent 
which is always directed toward N, opposes the motion and brings the 
pendulum to rest at E. It then retraces its path and continues to 
oscillate with a periodic and pendular motion. 

148. Definition of Terms. —The center of suspension is the 
point or axis about which the pendulum swings. A single 

vibration is the motion comprised between 
two successive passages of the pendulum 
through the lowest point of its path, as the 
motion from N to B (Fig. 128) and back 
to N again. A complete or double vibration 
is the motion between two successive pas¬ 
sages of the pendulum through the same 
point and going in the same direction. A 
complete vibration is double that of a 
single one. The period of vibration is the 
time consumed in making a complete or 
double vibration. The amplitude is the 
arc BN or the angle BAN 

149. Laws of the Pendulum. — T he following are the laws 
of a simple pendulum which are independent of both the 
material and the weight: 

I. For small amplitudes, the period of vibration is 
independent of the amplitude. 

II. The period of vibration is proportional to the square 
root of the length of the pendulum. 

III. The period of vibration is inversely proportional to 
the square root of the acceleration of gravity. 

One of the earliest and most important discoveries by 
Galileo was that of the experimental laws of the motion of 



me 

N 

Figure 128 . — 
Simple Pendu¬ 
lum. 




CENTER OF OSCILLATION 


139 


a pendulum, made when he was about twenty years of age. 
This was long before their theoretical investigation. 

If the period of a single vibration of a simple pendulum 
is denoted by t , the length by Z, and the acceleration of 
gravity by < 7 , it can be shown that 



(Equation 15) 


To illustrate Law I. It is only necessary to count the vibrations of 
a pendulum which take place in some convenient time with different 
amplitudes. Their number will be found to be the 
same. This result will hold even when the ampli¬ 
tudes are so small that the vibrations can only be ob¬ 
served with a telescope. 

To illustrate Law II. Mount three pendulums (Fig. 

129), making the lengths 1 m., £ m., and £ m. re¬ 
spectively. Observe the period of a single vibra¬ 
tion for each. They will be 1 sec., ^ sec., and | 
sec. nearly, or in periods proportional to the square 
root of the lengths. 

In accordance with Law III a pendulum 
oscillates more slowly on the top of a high 
mountain than at sea level, and more 
slowly at the equator than at the poles. 

Place a strong magnet just under the bob 
of the longest pendulum, which must be 
iron. It will then be found to vibrate in 
a slightly shorter period than before. The 
downward magnetic pull on the bob is 
equivalent to an increased value of g. 

150. Center of Oscillation. — Insert 
a small staple in one end of a meter stick, 
and suspend it so as to swing as a pendulum about a 
horizontal axis through the staple (Fig. 130). With a 
ball and a thread make a simple pendulum that will vi¬ 
brate in the same period as the meter stick. Beginning at 
the staple, lay off on the meter stick the length of this 


. Figure 129. 
— Pendulums 
of Different 
Lengths. 


Figure 
130.— 
C enter 
of Os¬ 
cillation. 








140 


MECHANICS OF SOLIDS 


pendulum. It will extend two thirds of a meter down. Bore a hole 
through the meter stick at the point thus found, and suspend it as a 
pendulum by means of a pin through this hole. Its period of vibration 
will be the same as before. 

The bar is a compound pendulum, and the new axis of 
vibration is called the center of oscillation. The distance 
between the center of suspension and the center of oscilla¬ 
tion is the length of the equivalent simple pendulum that 
vibrates in the same period as the compound pendulum. 
The centers of suspension and of oscillation are inter¬ 
changeable without change of period. 

151. Center of Percussion. — Suspend the meter bar by the staple 
at the end and strike it with a soft mallet at the center of oscillation. 
It will be set swinging smoothly and without perceptible jar. 

Hold a thin strip of wood a meter long and four or five centimeters 
wide by the thumb and forefinger near one end. Strike the flat side 
with a soft mallet at different points. A point may be found where 
the blow will not throw the wood strip into shivers, but will only set 
it swinging like a pendulum. 

The center of oscillation is also called the center of per¬ 
cussion; if the suspended body be struck at this point at 
right angles to the axis of suspension, it will be set swing¬ 
ing without jar. A baseball club or a cricket bat has a 
center of percussion, and it should strike the ball at this 
point to avoid breaking the bat and “ stinging ” the hands. 

152. Application of the Pendulum. — Galileo’s discovery 
suggested the use of the pendulum as a timekeeper. In 
the common clock the oscillations of the pendulum regulate 
the motion of the hands. The wheels are kept in motion 
by a weight or a spring, and the regulation is effected by 
means of the escapement (Fig. 131). The pendulum rod, 
passing between the prongs of a fork a, communicates its 
motion to an axis carrying the escapement, which ter- 


QUESTIONS AND PROBLEMS 


141 


minates in two pallets n and m. These pallets 
alternately with the teeth of the escapement wheel 
tooth of the wheel escaping from a pallet 
every double vibration of the pendulum. 

The escapement wheel is a part of the 
train of the clock; and as the pendulum 
controls the escapement, it also controls 
the motion of the hands. 

153. Seconds Pendulum. — A seconds pen¬ 
dulum is one making a single vibration in 
a second. Its length in New York is 
99.31 cm. This is the length of the 
equivalent simple pendulum vibrating sec¬ 
onds. The value of gravity g increases 
from the equator to the poles, and the 
length of the seconds pendulum increases 
in the same proportion. 


engage 
i2, one 



Questions and Problems 

1. Why can a heavy shot be thrown much 
farther by swinging it from the end of a short wire 
or cord than by hurling it from the shoulder as in 
“ putting the shot ” ? 

2. Why is the outer rail on a railway curve 
elevated above the inner one ? 



Figure 131. — Es¬ 
capement. 


3 . A ball weighing 10 lb. is attached to a cord 2 ft. long and is 
whirled about the hand at the rate of ten revolutions in three seconds. 
What is the tension in the cord ? 

4 . A ball swings as a conical pendulum; its mass is 2 kg., its 
distance from the center of its circular path is 30 cm., and it 
makes ten revolutions in 35 seconds. What horizontal force in 
grams would be necessary to hold the ball at any point in its path 
if it were not revolving ? 

5 . Find the period of vibration of a pendulum 70 cm. long, the 
value of g being 980 cm.-per-second per second. 










142 


MECHANICS OF SOLIDS 


6 . Calculate the length of a seconds pendulum at a place where 
the value of g is 980 cm.-per-second per second. 

7 . At a place where g is 32 ft.-per-second per second what is the 
length of a pendulum that vibrates in £ sec. ? 

8 . What would be the acceleration of gravity if a pendulum one 
meter long had a period of vibration of one second ? 

9 . If a simple pendulum 90 cm. long makes 64 single vibrations 
per minute, what is the value of < 7 ? 

10 . Two balls of the same diameter but of different materials and 
masses are suspended by threads of the same length and of negligible 
mass. If made to vibrate as pendulums, will their periods of vibra¬ 
tion differ and why ? 


CHAPTER VI 


MECHANICAL WORK 
I. WORK AND ENERGY 

154. Work. — A man does work in climbing a hill by lifting 
himself against the pull of gravity; a horse does work in drawing a 
wagon up an inclined roadway; a locomotive does work in hauling 
a train on the level against frictional resistances; gravity does work 
against the inertia of the mass when it causes the weight of a pile 



The Largest and Most Powerful Locomotive in the World. 


driver to descend with increasing velocity; steam does work on the 
piston of a steam engine and moves it by pressure against a resist¬ 
ance; the electric current does work by means of a motor when it 
drives an air compressor on an electric car and forces air into a com¬ 
pression tank. 

Mechanical work means the overcoming of resistance. 
Unless there is a component of motion in the direction in 
which the force acts in overcoming the resistance, no 
work in a physical sense is done. The columns in a mod¬ 
ern steel building do no work, though they sustain great 

143 





144 


MECHANICAL WORK 


weight; the pillars supporting a pediment over a portico 
do no work; a person holding a weight suffers fatigue, 
but does no work in the senses in which this word is used 
in physics, where it is employed to describe the result 
accomplished and not the effort made. 

155. Measure of Mechanical Work.—Mechanical work is 
measured by the product of the force and the displace¬ 
ment of its point of application in the direction in which 
the force acts, or 

work ==force x displacement . 

In symbols w __y x g # , . (Equation 16) 


Since force is equal to the product of mass and accelera¬ 
tion (§ 130), 

w = ma x s. . . . (Equation 17) 


156. Units of Work. — Before use can be made of these 
expressions for work, it is necessary to define the units 
employed in measuring work. Three or four such units 
are in common use : 

1. The foot pound (ft. lb.), or the work done by a 
pound of force working through a space of one foot. If 
a pound weight is lifted a foot high, or if a body is 
moved a distance of one foot by a force of one pound, a 
foot pound of work is done. This unit is in common use 
among English-speaking engineers. It is open to the 
objection that it is variable, since a pound of force varies 
with the latitude and with the elevation above sea level. 

2. The kilogram meter (kg. m.), or the work done by 
a kilogram of force working through a space of one 
meter. It is the gravitational unit of work in the metric 
system, and varies in the same manner as the foot pound. 
The gram-centimeter is also used as a smaller gravitational 


POWER 


145 


unit of work. The kilogram meter is equal to 100,000 
gram-centimeters. 

3. The erg} or the work done by a dyne working 
through a distance of one centimeter. The erg is the 
absolute unit in thee. g. s. system and is invariable. 

Since a gram of force is equal to 980 dynes (§ 115), if 
a gram mass be lifted vertically one centimeter, the work 
done against gravity is 980 ergs. Hence one kilogram 
meter is equal to 980 x 1000 x 100 = 98,000,000 ergs. 

The mass of a “nickel” is 5 g. The work done in lifting it 
through a vertical distance of 5 m. is the continued product of 5, 500, 
and 980, or 2,450,000 ergs. The erg is therefore a very small unit 
and not suitable for measuring large quantities of work. For such 
purposes it is more convenient to use a multiple of the erg, called the 
joule. 1 2 * Its value is 

1 joule = 10 7 ergs = 10,000,000 ergs. 

Expressed in this larger unit, the work done in lifting the 
“ nickel ” is 0.245 joule . 8 

157. Power. — While it takes time to do work, it is 
plain that time is not an element in the amount of work 
done. To illustrate: Suppose a ton of marble is lifted 
by a steam engine out of a marble quarry 300 ft. deep. 
The work is done by means of a wire rope, which the 
engine winds on a drum. If now the drum be replaced 
by another of twice the diameter, and running at the 
same rate of rotation, the ton of marble will be lifted in 
half the time; but the total work done against gravity 
remains the same, namely, 600,000 ft. lb. 

In an important sense the engine as an agent for doing 
work is twice as effective in the second instance as in the 

1 The erg is from the Greek word meaning work. 

2 From the noted English investigator Joule. 

8 The joule is equal to about f of a foot pound. 



346 


MECHANICAL WORK 


first. Time is an essential element in comparing the 
capacities of agents to do work. Such a comparison is 
made by measuring the power of an agent. Power tells 
us not how much work is done, but how fast it is done. 



A Marble Quarry. 


Power is the time rate of doing work , or 

work fxs /'T? . • ^ ox 

power = —— =* / -- • • • (Equation 18) 

txme t 

This expression may be used directly to measure power, 
due regard being paid to the units employed. The result 
will be in foot pounds per second, kilogram meters per 
second, gram-centimeters per second, or ergs per second, 
according to the consistent units used. 

The units of power universally used by engineers are 








POWER 


147 



Giant Ore Crane. 

When these jaws close, as shown in the picture on page 153, the bucket 
holds 12 tons of iron ore. 

either the horse power or the watt and its multiple the 
kilowatt. 

The horse power (H.P.) is the rate of working equal 
to 33,000 ft. lb. per minute, or to 550 ft. lb. per second. 













148 


MECHANICAL WORK 


Hence f v « 

HP -Arjr ' CE< '““ <,n 19) 

in which/is in pounds of force, s in feet, and t in seconds. 

In the c. g. s. system the watt 1 is the rate of working 
equal to one joule per second. A kilowatt (K.W.) is 
1000 watts. 

Hence watts = s - ; K.W. = ^ * * • (Equation 20) 
£ x 10 7 t x 10 10 v 1 J 

In Equation 20 / is in dynes, s in centimeters, and t 
in seconds. 

One horse power equals 746 watts, or 0.746 kilowatt 
(nearly -J K. W.). To convert kilowatts into horse powers 
approximately, add one third; to convert horse powers 
into kilowatts, subtract one fourth. For example, 60 K.W. 
are equal to 80 H.P., and 100 H.P. are equal to 75 K.W. 

The power capacity of direct current dynamo electric generators is 
now universally expressed in kilowatts; the steam engines and water 
turbines used to drive these generators are commonly rated in the same 
unit of power; so, too, the capacity of electric motors is more often 
given in kilowatts than in horse powers. A kilowatt hour means power 
at the rate of a kilowatt expended for one hour. Thus, 20 kilowatt 
hours mean 20 K.W. for one hour, or 5 K.W. for four hours, etc. 

158. Energy. — Experience teaches that under certain 
conditions bodies possess the capacity for doing work. 
Thus, a body of water at a high level, gas under pressure 
in a tank, steam confined in a steam boiler, and the air 
moving as a wind, are all able to do work by means of 
appropriate motors. In general, a body or system on which 
work has been done acquires increased capacity for doing 
work. It is then said to possess more energy than before. 


1 From the noted English engineer James Watt. . 






POTENTIAL ENERGY 


149 


“Work may be considered as the transference of energy 
from one body or system to another.” “ Energy we know 
only as that which in all natural phenomena is constantly 
passing from one portion of matter to another.” Since 
the work done on a body is the measure of its increase 
of energy, work and energy are measured in the same 
units. 

159. Potential Energy. — A mass of compressed air in 
an air gun tends to expand; it possesses energy and may 
expend it in propelling a bullet. 

Energy is stored also in the lifted 
weight of the pile driver (Fig. 

182), the coiled spring of the 
clock, the bent bow of the archer, 
the impounded waters behind a 
dam, the chemical changes in a 
charged storage battery, and the 
mixed charge of gasoline vapor 
and air in the cylinder of a gas 
engine. 

In all such cases of the storage 
of energy a stress (§ 43) is pres¬ 
ent. The compressed air pushes 
outward in the air gun; gravity 
pulls on the lifted weight; the 
spring tends to uncoil in the clock; the bent bow tries to 
unbend; the water presses against the dam ; the electric 
pressure is ready to produce a current; and the explosive 
gas mixture awaits only a spark to set free its energy. 
The energy thus stored, which is associated with a stress or 
with a position with respect to some othe body, is energy 
of stress , or, more commonly, potential energy. The energy 
of an elevated body, of bending, twisting, of chemical sep 



Figure 132 . — Pile Driver. 







150 


MECHANICAL WORK 


aration, and of air, steam, or water under pressure, are all 
examples of potential energy. 

160. Kinetic Energy. — A body also possesses energy in 
consequence of its motion; the energy of a moving body 
is known as kinetic energy. The descending hammer forces 
the nail into the wood, the rushing torrent carries away 
bridges and overturns buildings ; the swiftly moving can¬ 
non ball, by virtue of its high speed, demolishes fortifica¬ 
tions or pierces the steel armor of a battleship ; the energy 
stored in the massive rotating flywheel keeps the engine 
running and may do work after the steam is shut off. 
When the engine is speeding up, it pushes and pulls on 
the shaft to increase the speed of the flywheel; in other 
words, the engine does work on the flywheel. After 
normal speed has been reached, all the work done by the 
engine goes into the driven machinery; but if an extra 
load comes on the engine, its speed does not drop sud¬ 
denly, because it is sustained by the flywheel giving out 
some of its stored energy to help along the engine. The 
engine tends to stop the flywheel, and this now does work 
instead of absorbing energy. 

When a meteoric body, or “ shooting star,” enters the 
earth’s atmosphere, its energy of motion is converted into 
heat by friction with the air; the heat generated raises 
the temperature of the meteor (at least on its surface) 
until it glows like a star. If it is small, it may even burn 
up or become fine powder. 

The energy of the invisible molecular motions of bodies 
constituting heat is included under kinetic energy no less 
than that of their visible motion. Heat is a form of 
kinetic energy. 

Kinetic energy must not be confused with force. A 
mass of moving matter carries with it kinetic energy, but 



United States 16-inch Gun from the Watervliet Arsenal 













































































Or 














































KINETIC ENERGY 


151 


it exerts no force until it encounters resistance. Energy 
is then transferred to the opposing body, and force is 
exerted only during the transfer. 

161. Measure of Energy. — Energy is measured in the 
same terms as those used in measuring work. In general, 
potential energy is the measure of the mechanical work 
done in storing the energy, or 

P.l=/x 8. . . (Equation 21) 

If f is in pounds of force and s in feet, the result is in 
foot pounds. Similarly, if f is in grams of force and s 
in centimeters, the potential energy is expressed in gram- 
centimeters. 

Since a gram of force is equal to 980 dynes, expressed 
in ergs, p p] _ 939 x grams x centimeters. 

162. Kinetic Energy in Terms of Mass and Velocity. — 

The work fs done by the force f on the mass m to give it 
the velocity v, while working through the distance s, 
measures the kinetic energy acquired, or, 

K.E. =fxs. 

But it is highly desirable to express kinetic energy in 
terms of the mass m and the acquired velocity v, instead 
of f and s. By the second law of motion (§ 130)/ = ma. 
Hence K.E. — ma x s. But s = \at 2 . Therefore K.E. = 
\ma 2 t 2 . Also v = at (§ 106); therefore 

K.E. — \mv 2 . . . (Equation 22) 

Both m and v are magnitudes independent of gravitation ; 
it follows that the results calculated from Equation 22 can¬ 
not be in gravitational units. If m is expressed in grams 
and v in centimeters per second, the kinetic energy is in 


152 


MECHANICAL WORK 


ergs. Since the gram-centimeter is equal to 980 ergs, to 
reduce the result to gram-centimeters, divide by the value 
of g in this system, or 980. 

In precisely the same way, if m is in pounds and v in 
feet per second, to obtain the energy in foot pounds, 
divide by the value of g in the English system, 82.2. 


To illustrate: If an automobile, weighing 3000 lb., is running at a 
speed of 30 miles per hour, find its kinetic energy. 

A mile a minute is 88 ft. per second, and 30 miles an hour or half 
a mile a minute is 44 ft. per second. Hence the kinetic energy of the 
moving car is 

90,186 ft. lb. 


3000 x 44 2 


2 x 32.2 


This energy represents very nearly the work required to lift the car 
30 ft. high against gravity, for this work is 

3000 x 30 = 90,000 ft. lb. 

A large ship, moving toward a wharf with a motion scarcely per¬ 
ceptible, will crush with great force small intervening craft. The 
moving energy of the large vessel is great because of its enormous 
mass, even though its velocity is small. Its weight is supported by 
the water and has nothing to do with its crushing force. 


163. Transformations of Energy. — When a bullet is shot 
vertically upward, it gradually loses its motion and its 
kinetic energy, but gains energy of position or potential 
energy. When it reaches the highest point of its flight, 
its energy is all potential. It then descends, and gains 
energy of motion at the expense of energy of position. 
The one form of energy is, therefore, convertible into the 
other. 

The pendulum illustrates the same principle. While 
the bob is moving from the lowest point of its path 
toward either extremity, its kinetic energy is converted 
into potential energy; the reverse transformation sets in 



DISSIPATION OF ENERGY 


15a 



when the pendulum reverses its motion. All physical 
processes involve energy changes, and such changes are 
in ceaseless progress. 

164. Conservation of Energy. — Whenever a body gains 
energy as the result of work done on it, it is always at the 
expense of energy in 
some other body or 
system. The agent, 
or body, which does 
work always loses 
energy; the body 
which has work done 
on it gains energy 
equal to the work 
done. On the whole 
there is neither gain 
nor loss of energy, 
but only its transfer 
from one body to an¬ 
other. Innumerable 
facts and observa¬ 
tions show that it is 


as impossible to ere- Closed Jaws of Ore Bucket. 

ate energy as it is This crane makes one trip per minute from 
to create matter. So the hold of the vessel t0 the ore train on the 
the law of conserva¬ 
tion of energy means that no energy is created and none 
destroyed by the action of forces we know anything about. 

165. Dissipation of Energy. — Potential energy is the 
more highly available or useful form of energy. It always 
tends to go over into the kinetic type, but in such a way 
that only a portion of the kinetic energy is available to 
effect useful changes in nature or in the mechanic arts. 






154 


MECHANICAL WORK 


The remainder is dissipated as heat. This running down 
of energy by passing into an unavailable form is known as 
the dissipation of energy . It was first recognized and dis¬ 
tinctly stated by Lord Kelvin in 1859. 

The capacity which a body possesses for doing work 
does not depend on the total quantity of energy which it 
may possess, but only on that portion which is available, 
or is capable of being transferred to other bodies. In the 
problems of physics our chief concern is with the varia¬ 
tions of energy iji a body and not with its total value. 

Questions and Problems 

1. A cord that will just support an iron ball will generally break 
if the attached ball is lifted and allowed to drop. Explain. 

2. In what form is the energy of a coiled spring? Of a bomb? 
Of a pile driver ? 

3 . Lake Tahoe in the Sierra Nevadas is at an elevation of 6225 ft. 
above the sea. Account for the energy of position stored there in the 
water. 

4 . Why has the ball in leaving the gun so much more energy of 
motion than the gun has in the recoil ? 

5 . Why is “ perpetual motion ” impossible? 

6. Is not the case of the earth going around the sun a case of 
perpetual motion? How does this differ from what is commonly 
meant by “ perpetual motion ” ? 

7 . A man weighing 200 lb. climbs to the top of a hill 900 ft. 
high. How much work does he do ? 

8. A man carries a ton of coal up a flight of stairs 14 ft. high. 
How much work does he do ? 

9. A force of 200 dynes moves a mass of 100 g. through a dis¬ 
tance of 50 cm. How much work is done ? 

10 . A load of two tons was drawn up a hill half a mile long by a 
traction engine. The hill was 100 ft. high. How much work was 
done? What force did the engine exert? 

Suggestion. — Notice that the work done by the engine in pulling the 
load half a mile is the same as lifting it vertically 100 ft. 



Lord Kelvin (Sir William Thomson), 1824-1907, was born 
at Belfast. He graduated at Cambridge in 1845 and in the same 
year received the appointment of professor of natural philosophy 
in the University of Glasgow, a position which he held for fifty- 
three years. He was one of the greatest mathematical physicists 
of his day. His invention of the astatic mirror galvanometer and 
the siphon recorder has made successful marine cables a reality. 
His laboratory for the use of students was the first of the kind to 
be established. His most noteworthy investigations were in heat, 
energy, and electricity, yet there is scarcely any portion of physi¬ 
cal science that has not been greatly enriched by his genius. 


















WHAT A MACHINE IS 


155 


11 . How much work can a 40 H.P. engine do in an hour? How 
many tons of coal can it raise out of a mine 400 ft. deep in 10 hours ? 

12. Express in joules the work done by a force of 100 kg. in mov¬ 
ing 100 kg. through a distance of 100 km. 

13 . An electric motor rated at 100 K.W. is used to operate a pump. 
The water has to be raised 100 m. How many .liters will it be pos¬ 
sible to pump per hour ? 

14 . The mass of a railroad train is 250 tons, and the resistance to its 
motion on a level track is 15 lb. per ton. What H.P. must the loco¬ 
motive develop to maintain a speed of 40 miles per hour on the level ? 

15 . What is the potential energy of a stone weighing 100 lb. as it 
rests on the top of a column 50 ft. high ? What will be its kinetic 
energy at the moment of reaching the ground if it should fall ? How 
much work would be done in placing the stone back on the column ? 

16 . A ball with a mass of 100 g. is given a velocity of 100 m. per 
sec. by being struck with a club. What was the energy of the blow ? 

17. An automobile weighing 2500 lb. when running at the rate of 30 
mi. an hour strikes a telephone pole. Calculate the energy of the blow. 

18 . A force of 100 g. moves a mass 1000 g. through a distance of 
100 m. in 10 sec. Express the activity of the agent in watts. 

19 . The mass of the ram of a certain pile driver is 2000 lb. It 
falls from a height of 20 ft. upon the head of a pile and drives it 2 ft. 
into the ground. What is the energy of the blow delivered to the 
pile ? What is the resistance offered by the ground ? 

20 . A cannon ball weighing 10 lb. is fired from a cannon whose 
barrel is 5 ft. long with a velocity of 1500 ft. per sec. Calculate the 
momentum of the ball; also the energy of the ball; also the average 
force acting on the ball in the barrel. 

II. MACHINES 

166. What a Machine is. — A machine is a device designed 
to change the direction or the value of a force required to 
do useful work, or one to transform and transfer energy. 

Simple machines enable us to do many things that would be impos¬ 
sible for us to do without them. A boy can draw a nail with a claw 


156 


MECHANICAL WOEK 


hammer (Fig. 133) ; without it and with his fingers alone he could 
not start it in the least. By the use of a single pulley, the direction 
of the force applied may be changed, so as to lift a 
weight, for example, while the force acts in any 
convenient direction. Two men can easily lift a 
piano up to a second story window with a rope and 
tackle. Perhaps the most important use of machines 
is for the purpose of utilizing the forces exerted by 
animals, and by wind, water, steam, or electricity. 
A water wheel transforms the potential and kinetic 
energy of falling water into mechanical energy rep¬ 
resented by the energy of the rotating wheel. A 
dynamo electric machine transforms mechanical 
energy into the energy of an electric current, and an electric motor 
at a distance transforms the electric energy back again into useful 
mechanical work. 

167. General Law of Machines. — Every machine must 
conform to the principle of the conservation of energy ; 
that is, the work done by the applied force equals the work 
done in overcoming the resistance, except that some of the 
applied energy may be dissipated as heat or may not 
appear in mechanical form. A machine can never produce 
an increase of energy so as to give out more than it 
receives. 

Denote the applied force, or effort , by E and the resist¬ 
ance by E, and let 1) and d denote the distances respectively 
through which they work. Then from the law of conser¬ 
vation of energy, the effort multiplied by the distance 
through which it acts is equal to the resistance multiplied 
by its displacement, or 

ED = Ed. . . . (Equation 23) 

168. Friction. — Friction is the resistance which opposes an 
effort to slide or roll one body over another. It is called into 
action whenever a force is applied to make one surface 



Figure 133.— 
Hammer as Lever. 



FRICTION 


157 


move over another. Friction arises from irregularities in 
the surfaces in contact and from the force of adhesion. 
It is diminished by polishing and by the use of lubricants. 

Experiments show that friction (a) is proportional to 
the pressure between the surfaces in contact, (6) is inde- 



Machine for Measuring Friction at Mass. Inst, of Technology. 


pendent of the area of the surfaces in 
tain limits, and (<?) has its greatest 
motion takes place. The friction of a 
solid rolling on a smooth surface is 
less than when it slides. Advantage 
is taken of this fact to reduce the fric¬ 
tion of bearings. A ball-bearing (Fig. 
134) substitutes the rolling friction 
between balls and rings for the sliding 
friction between a shaft and its journal. 


contact within cer- 
value just before 



Figure 134 . — Ball¬ 
bearing. 







158 


MECHANICAL WORK 




Roller bearings (Fig. 
135) are also used with 
similar advantages. 

169. Advantages and 
Disadvantages of Friction. 
— Friction has innumer¬ 
able uses in preventing 
motion between surfaces 
in contact. Screws and 
Figure 135 . -Roller Bearing. nails hold entirely by 

friction; we are able to walk because of friction between 
the shoe and the pavement; shoes with nails in the heels are 
dangerous on cast-iron plates because the friction between 
smooth iron surfaces 
is small. Friction is 
useful in the brake 
to stop a motor car 
or railway train, in 
holding the driving 
wheels of a locomo¬ 
tive to the rails, and 
in enabling a gaso¬ 
line engine to drive 
an automobile by 
friction between the 
tires and the street. 

On the other hand, 
friction is also a re¬ 
sistance opposing 
useful motion, and 
whenever motion 
takes place, work 
must be done against 


Caterpillar Tractor. 

The chain belt around the wheels greatly in¬ 
creases the friction with the ground. 






SIMPLE MACHINES 


159 


this frictional resistance. The energy thus consumed is 
converted into heat and is no longer available for useful 
work. 

170. Efficiency of Machines. — On account of the impos¬ 
sibility of avoiding friction, every machine wastes energy. 
The work done is, therefore, partly useful and partly waste¬ 
ful . The efficiency of a machine is the ratio of the useful 
work done by it to the total work done by the acting force , 


or 


efficiency = 


useful work done 
total energy applied 


For example, an effort of 100 pounds of force applied to a machine 
produces a displacement of 40 ft. and raises a weight of 180 lb. 20 ft. 
high. Then 100 x 40 = 4000 ft. lb. of energy are put into the ma¬ 
chine, and the work done is 180 x 20 = 3600 ft. lb. 

Hence efficiency = = 0.9 = 90 per cent. 

* U 4000 F 

Ten per cent of the energy is wasted and ninety per cent recovered. 


Since every machine wastes energy, a machine which 
will do either useful or useless work continuously without 
a supply of energy from without, a so-called “perpetual 
motion machine,” is thus clearly impossible. 

' Let e denote the efficiency of a machine; then from the 
relations just explained, Equation 23 becomes 

eED = J Rd. . . . (Equation 24) 

This relation is the strictly correct one to apply to all 
machines; but in most problems dealing with simple 
machines, friction is neglected. 

171. Simple Machines. — All machines can be reduced to 
six mechanical powers or simple machines: the lever, the 
pulley, the inclined plane, the wheel and axle, the wedge, 
and the screw . Since the wheel and axle is only a modi- 



160 


MECHANICAL WOBK 


fied lever, and the wedge and the screw are modifications 
of the inclined plane, the mechanical powers may be re¬ 
duced to three. 

In solving problems relating to simple machines in ele¬ 
mentary physics it is customary to neglect friction and to 
consider that the parts of machines are rigid and without 
weight. With these limitations, the law expressed by 
Equation 23 holds good. 

172. Mechanical Advantage. —A man working a pump 
handle and pumping water is an agent applying energy; 
the pump and the water compose a system receiving energy. 
In a simple machine the force exerted by the agent ap¬ 
plying energy, and the opposing force of the system re¬ 
ceiving energy, may be denoted by the two terms, effort , 
E , and resistance , R. The problem in simple machines 
consists in finding the ratio of the resistance to the 
effort. 

The ratio of the resisting force R to the applied force E 
is called the mechanical advantage of the machine. This 
ratio may always be expressed in terms of certain parts of 
simple machines. 

173. Moment of a Force.— In the application of the 
lever, the pulley, or the wheel and axle there is motion 
about an axis. The application of a single force to a body 
with a fixed axis produces rotation only. Examples are a 
door swinging on its hinges and the flywheel of an engine. 

The effect of a force in producing rotation depends, not 
only on the value of the force, but on the distance of its 
line of application from the axis of rotation. A smaller 
force is required to close a door when it is applied at right 
angles to the door at the knob than when it is applied 
near the hinge. Also, an increase in the speed of rota¬ 
tion of a flywheel may be secured either by increasing the 


THE LEVEE 


161 


M 


Figure 136 — Mo¬ 
ment of Force. 


applied force or by lengthening the crank. Both these 
elements of effectiveness are included in what is known as 
the moment of a force. 

The moment of a force is the product of 
the force and the perpendicular distance 
between its line of action and the axis of 
rotation . Let M be a body which may 
rotate about an axis through 0 (Fig. 

136). The moment of the force F ap¬ 
plied at B in the direction CB is F x OB ; 
applied in the direction AB, its moment 
is F x OA. The point 0 is called the 
center of moments. 

A moment is considered positive if it produces rotation 
in a clockwise direction, and negative if in the other. If 
the sum of the positive moments equals that of the negative 
moments , there is equilibrium. 

The principle of moments is a very useful one in solv¬ 
ing a great variety of problems. 

_ 174. The Lever.—The lever 

is more frequently used than 
any other simple machine. In 
its simplest form the lever is a 
rigid bar turning about a fixed 
axis called the fulcrum. It is 
convenient to divide levers into 
three classes, distinguished by 
the relative position of the ful¬ 
crum with respect to the two 
forces. In the first class the 
fulcrum is between the effort 


EJL 


Figure 137 . —Levers. 


E and the resistance R (Fig. 137) ; in the second class 
the resistance is between the effort and the fulcrum ; in 















162 


MECHANICAL WOBK 



Figure 138. — Lever, 
First Class. 


the third class the 
effort is between 
the resistance and 
the fulcrum. 



F 

Figure 139.— Lever, 
Second Class. 



Figure 140. — Scis¬ 
sors. 



175. Examples of Levers. — A crowbar 
used as a pry (Fig. 138) is a lever of the first 

class, but when used to lift a weight with one 
end on the ground (Fig. 139), it is a lever of the 
second class. Scissors (Fig. 140) are double 
levers of the first 
class. So also 
are the tongs of 
a blacksmith, and those used in chemi¬ 
cal laboratories for lifting crucibles 
(Fig. 141). The forearm when it supports a weight in the extended 

hand (Fig. 142), and the door when 
it is closed by pushing it near the 
hinge, are examples of levers of the 
third class. 

Nut - crack¬ 
ers (Fig. 

143) and 


Figure 141. —Tongs. 



Figure 



Figure 143. — Nut 
Cracker. 


lemon squeezers are double levers of the second 
class. 

The steelyard (Fig. 144) is a lever of the first class with unequal 
arms. The common balance (Fig. 145) is a lever of the 


first class with equal arms, 
also equal. The conditions 



The two weights are thus 
for a sensitive balance, to 
show a small excess of 
weight in one pan over 
that in the other, are small 
friction at the fulcrum, a light beam, and 
the center of gravity only slightly lower 
than the “ knife-edge ” forming the ful¬ 
crum. 

Figure 144 F76. ^ ec ^ an i ca l Advantage °f the Lever. —In 

Steelyard. Fig. 146 E is the effort, B the resistance or 











MECHANICAL ADVANTAGE OF THE LEVER 163 



weight lifted, C the fulcrum, and AC and BC the lever 
arms. Consider the lever to be weightless and to rotate 
about C without fric¬ 
tion ; then the moment 
of the force E about 
the fulcrum (§ 173) is 
E x A C, and that of the 
force R is R x BC. 

These two forces tend to 
produce rotation in op¬ 
posite directions ; for 
equilibrium their mo¬ 
ments are therefore FlGURE 145. -Common Balance. 

equal, that is, ExAC*=RxBC\ from which 

R^AC 
E BC 
(Equation 25) 

Hence, the mechanical 
advantage of the lever 
equals the inverse ratio 
of its arms. 

If the weight of the 
lever has to be taken into account, it is to be treated as a 

force acting at the center . 

, . ° 1 a o , B 

of gravity of the lever, and r~ r ~ T ~ 

its moment must be added 
to that of the force turning 
the lever in the same direc¬ 
tion as its own weight. 

Example. The weights W 1 
and W 2 are placed at distances 
5 and 8 units respectively from 0 (Fig 
must W 2 be for equilibrium ? 




XR 

Figure 146 . — Mechanical Advantage of 
Lever. 


H f f 




Figure 147 . 


147). If W x is 20 lb., what 
By the principle of moments about O, 
















164 


MECHANICAL WORE 


20 x 5 = W 2 x 8; 

whence W 2 = 12.5 lb. 

If the lever is uniform, it is balanced about the fulcrum 0 and its 
moment is zero. Suppose the weight of the bar to be 1 lb. and its 
center of gravity 4 units to the left of 0. The equation for equi¬ 
librium would then be 

20x5+1 x 4 = W 2 x 8. 

Whence IT, =13 lb. 

177. The Wheel and Axle consists of a C}dinder and a 
wheel of larger diameter usually turning together on the 
same axis. In Fig. 148 the axle passes through (7, the 
radius of the cylinder is BO , and that of the wheel is 

AC. The weights P and W are sus¬ 
pended by ropes wrapped around the cir¬ 
cumference of the two wheels; their 
moments about the axis 0 are P x AO 
and W x BO respectively. For equilib¬ 
rium these moments are equal, that is, 
w P xAO=WxBC. Hence, 

W AO 7? 

Figure 148.— — = • (Equation 26) 

Wheel and Axle. P BO r 

R and r are the radii of the wheel and the axle respec¬ 
tively. The weight P represents the 
effort applied at the circumference of 
the wheel, and the weight W the resist¬ 
ance at the circumference of the axle. 

Therefore, the mechanical advantage of 
the wheel and axle is the ratio of the 
radius of the wheel to that of the axle. 

178. Applications. — The old well wind¬ 

lass for drawing water from deep wells (Fig. Figure 149. — Well 
149) by means of a rope and bucket is au ap- Windlass. 















THE PULLEY 


165 


plication of the principle of the wheel 
and axle. In the windlass a crank takes 
the place of a wheel and the length of 
the crank is the radius of the wheel. 

In the capstan (Fig. 150) the axle is 
vertical, and the effort is applied by 
means of handspikes inserted in holes 
in the top. 



The derrick (Fig. 151) is a form of 
wheel and axle much used for raising 

heavy weights. 


Figure 150 . — Capstan 



Figure 151 . — Derrick. 


In the form shown 
it is essentially a double wheel 
and axle. The axle of the first sys¬ 
tem works upon the wheel of the 
second by means of the spur gear. 
The mechanical advantage of such a 
compound machine is the ratio of the 
product of the radii of 
the wheels to the product 
of the radii of the axles. 

In the case of gearing, 
the number of teeth is 
substituted for the ra¬ 
dius. 

of a wheel , called a 




179. The Pulley consists 
sheave , free to turn about an axle in a frame , 
called a block (Fig. 152). 

The effort and the resist¬ 
ance are attached to a rope 
which moves in a groove cut 
in the circumference of the wheel. 


Figure 152 . 
— Block and 
Sheave. 


0 

W y E 

Figure 153 . — Single 
Pulley. 


simple fixed pidley is one whose axis 
does not change its position; it is used 
to change the direction of the applied 
force (Fig. 153). If friction and the 
rigidity of the rope are neglected, the 
tension in the rope is everywhere the 













166 


MECHANICAL WORK 



Practical Use of Derricks. 

These enormous derricks are used for raising the huge blocks of marble 
from the quarry. 


v 


E 



Figure 154 . — Mov¬ 
able Pulley. 


same ; the effort and the resistance are 
then equal to each other and the 
mechanical advantage is unity. 

In the movable pulley (Fig. 154) it 
is evident that the weight W is sup¬ 
ported by two parts of the cord, one 
half of it by means of the hook fixed 
in the beam above and the other half 
by the effort E applied at the free end 
of the cord. If the weight is lifted, it 
rises only half as fast as the cord 
travels. 

180. Systems of Fixed and Movable 
Pulleys. — Fixed and movable pulleys 











MECHANICAL ADVANTAGE OF SIMPLE PULLEY 167 


are combined in a great variety of ways. The most com¬ 
mon is the one employing a continuous cord with one free 
end and the other attached to a rigid 
support or to one of the blocks. Figure 
155 represents a combination of one fixed 
and one movable pulley. Figure 156 il¬ 
lustrates the common “ block and tackle,” 
where each block has more than one sheave. 

181. Mechanical Advantage of the Simple 
Pulley. — In Fig. 157 the cord passes in 
succession around each pulley. It is evi¬ 
dent that if the movable 
pulley and the resistance. 

W are moved toward the 
fixed pulley a distance a, Fixed and Mov- 
each cord passing between ABLE PuLLEYS - 
the two blocks must be shortened by a 
units. The effort E therefore travels 
through a distance of na units, n being the 
number of parts to the cord between the 
two pulleys. Then by the general law of 
machines (§ 167), 

E xna = W X a ; 

W 

whence — = n. (Equation 27) 

E 

Hence, when a continuous cord is used , the 
mechanical advantage of the pulley is equal 

Figure 156.— to the number of times the cord passes to 
Block and Tackle. from the movable block. 

It should be noticed that n is equal to the entire num¬ 
ber of sheaves in the fixed and movable blocks, or to that 








168 


MECHANICAL WORK 



Figure 157.— 
Multiple Pul¬ 
leys. 


number plus one. If the upper block in 
Fig. 157 were the movable one, that is, if 
the system were inverted, so that the effort 
E is upward, n would be equal to one more 
than the number of sheaves. 

182. The Differential Pulley.—The differ¬ 
ential pulley (Fig. 158) is much used for 
lifting heavy machinery by means of a rela¬ 
tively small force. 

In the upper block 
are two sheaves of 
different diameters 
turning rigidly to¬ 
gether. The lower 
block has only one 
sheave. An end¬ 
less chain runs over 
the three sheaves 
in succession. It 
is kept from slip¬ 


ping by projections on the sheaves, 
which fit between the links of the 
chain. A practical advantage of 
the differential pulley is that 
there is alwaj^s enough friction to 
keep the weight from dropping 
when there is no force applied to 
the chain. 

The mechanical advantage of the dif¬ 
ferential pulley may be found as follows: 
In Fig. 159, which is an outline drawing 
of this pulley, let the radius A C of the 
larger sheave be denoted by R, and that 



Figure 


158. — Differential 
Pulley. 















TEE INCLINED PLANE 


169 


of the smaller one AB by r. Suppose a force E to move the chain some 
convenient distance as R ; then a length r winds off the smaller sheave 
at B and a length R winds on the larger sheave at 
D. The length of chain between the two blocks is 
thus shortened by a length R — r, and the weight W 
is lifted a distance %(R — r ). The work done by 
the effort E is E x R and the work done on W is 
W x l(R - r). Neglecting friction, these expres¬ 
sions may be placed equal to each other, or 

E x R = Wx l(R -r). 

Whence — . . (Equation 28) 

E R — r 

Since the difference R — r may be made small, it 
is obvious that the mechanical advantage of the dif¬ 
ferential pulley is large, and it is larger the nearer r 
approaches R in length. 


183. The Inclined Plane. — Any plane surface making an 
angle with the horizontal is an inclined plane. Planks or 



Figure 160. — Huge Floating Crane. 



Outline of Dif¬ 
ferential Pul¬ 
ley. 















170 


MECHANICAL WORK 


skids used to roll casks and barrels up to a higher level are 
examples of inclined planes. Every road, street, or railway 
not on a level is an inclined plane. The steeper the incline, 
the greater the push required to force the load up the grade. 

If a body rests on an inclined plane without friction, 
the weight of the body acts vertically downward, while 
the reaction of the plane is perpendicular to its surface, 
and therefore a third force must be applied to maintain 
the body in equilibrium on the incline. 

184. Mechanical Advantage of the Inclined Plane. — Con¬ 
sider only the case in which the force applied to maintain 

equilibrium is parallel to the 
face of the plane (Fig. 161). 

The most convenient way 
to find the relation between 
the force E and the weight 
W of the body D is to apply 
the principle of work(§ 167). 
Suppose D to be moved by 
the force E from A to <7. Then the work done by E is 
E x AC. Since the body J) is lifted through a vertical dis¬ 
tance BC , the work done on it against gravity is Wx BC. 
Therefore, E xAC— Wx BC, and 



Figure 161. — Inclined Plane. 


w 

E 


AC 

BC 


(Equation 29) 


or the mechanical advantage, when the effort is applied parallel 
to the face of the plane, is the ratio of the length of the plane 
to its height. 

185. Grades. — The grade of an inclined roadway is ex¬ 
pressed as the number of feet rise per hundred feet along 
the incline. If the rise, for example, is 3 feet for every 
100 feet measured along the roadway, the road has a three 





GRADES 


171 



per cent grade. The grade of railways seldom exceeds 
2 per cent, but county roads and state highways may have 
8 or 10 per cent grades. Various expedients are adopted 
for the purpose of lengthening the incline on roads and 
railways so as to keep the grades within practical limits. 


The Great Pyramid. 

The huge stones of which the pyramids are made were probably raised to 
their great height by inclined planes. 

Zigzags and “switchbacks” are common expedients for 
the purpose. 

A most remarkable inclined railway track is on the 
northern approach to the St. Gotthard tunnel in Switzer¬ 
land. This tunnel reaches a culminating elevation of 3786 
feet. In at least one instance the railway forms three turns 
of a screw, one above the other, each turn lying partly 
on the face of the mountain and partly in a tunnel cut 



172 


MECHANICAL WORK 


through the rock. This novel grade enables the road to 
surmount a precipice by means of an inclined plane, the 
necessary length of which was secured along the thread of 
a mammoth screw. 

186. The Wedge is a double inclined plane with the 
effort applied parallel to the base of the plane, and usually 
by a blow with a heavy body (Fig. 162). Although the 

principle of the wedge is 
the same as that of the 
inclined plane, yet no ex¬ 
act statement of its me¬ 
chanical advantage is pos¬ 
sible, because the resistance 
has no definite relation to 
the faces of the planes, and the friction cannot be neglected. 
Many cutting instruments, such as the ax and the chisel, 
act on the principle of the wedge ; 
also nails, pins, and needles. 

187. The Screw is a cylinder, 
on the outer surface of which is a 
uniform spiral projection, called 
the thread. The faces of this 
thread are inclined planes. If a 
long triangular strip of paper be 
wrapped around a pencil (Fig. 163), with the base of the 
triangle perpendicular to the axis of the cylindrical pencil, 

the hypotenuse of the triangle 
will trace a spiral like the thread 
of a screw. 

The screw (Fig. 164) works in 
a block called a nut, on the inner 
surface of which is a groove, the 
exact counterpart of the thread. 



Figure 164. — The Nut. 




Figure 162. — The Wedge. 












I 


APPLICATIONS OF THE SCREW 


173 



Figure 165. — Pitch of Screw. 


The effort is applied at the end of a lever or wrench, 
fitted either to the screw or to the nut. When either 
makes a complete turn, the screw or the nut moves through 
a distance equal to that between two adjacent threads, 
measured parallel to the axis 
of the screw cylinder. This 
distance, s in Figure 165, is 
called the pitch of the screw. 

It is usually expressed as the 
number of threads to the inch 
or to the centimeter. 

188. Mechanical Advantage of 
the Screw. — Since the screw is usually combined with the 

lever, the simplest method of finding 
the mechanical advantage is to apply 
the principle of work, as expressed in the 
general law of machines (§ 167). If the 
pitch be denoted by s and the resistance 
overcome by R, then, ignoring friction, 
the work done against R in one revolu¬ 
tion of the screw is R x s. If the length 
Figure 166. — Jack- of the lever is l , the work done by the 
screw. effort E in one revolution is E x 2 irl. 

Whence E x ZttI=R x *, or 

:§= — • (Equation 30) 

Jbj s 

Hence, the mechanical advantage of 
the screw equals the ratio of the dis¬ 
tance traversed by the effort in one 
revolution of the screw to the pitch of Figure 167. — Letter 
the screw. Press. 

189. Applications of the Screw. — The jackscrew (Fig. 166), the 
letter press (Fig. 167), the vise (Fig. 168), the two blade propeller of a 










174 


MECHANICAL WORK 



Figure 168 . —■ 
The Vise. 


flying machine, and the two, three, or four blade propeller of a ship 
are familiar examples of the use of a screw. The rapid rotation of 
the propeller blades tends to push backward the air 
in the one case and the water in the other, but the 
inertia of the fluid medium produces a reaction 
against the propeller and forces the vessel forward. 
The screw propeller pushes against the fluid and so 
forces itself and the vessel to which it is attached in 
the other direction. 

An important application of the screw’, though not 
as a machine, is that for measuring small dimensions. The wire 
micrometer (Fig. 169) and th espherometer 
(Fig. 170) are instruments for this pur- 
pose. In both, an accurate screw has a 
head divided into a number of equal 
parts, 100 for example, so as to register 
any portion of a revolution. If the pitch 
of the screw is 1 mm., then turning the 
head through one of its divisions causes 
the screw to move parallel to its axis 
0.01 mm. All wood screws, augers, gimlets, find most machine screws 
and bolts are right-handed, — that is, they 
screw in or away from the observer by turn¬ 
ing around in the direction of watch hands. 
An example of a left-handed screw is the 
turnbuckle (Fig. 171). This has a right- 
handed screw at one end and a left-handed 
screw at the other. It is used for tightening 
tie rods, stays, etc. One turn of the buckle 
brings the rods together a distance equal to 
twice the pitch of the screws. 



Figure 169 . — Micrometer. 



Figure 170 . —Spherome- 
ter. 


Questions and Problems 


1. What are the relative positions of the effort, the resistance, 
and the fulcrum in the following: the lever as applied to the jack- 
screw, the oar of a boat in row¬ 
ing, the claw hammer in pull¬ 
ing a nail, and a bar applied to 

a car wheel to move the car? Figure 171. — Turnbuckle. 








































QUESTIONS AND PROBLEMS 


175 


2. In which direction does friction on the rails act on the 
wheels of a locomotive? On those of a freight car? Does it act in 
the same direction on the front and rear wheels of an automobile ? 

3 . Calculate the efficiency of a machine that lifts a weight of 1000 
lb. a distance of 8 ft. by the action of a force of 100 lb. through 100 ft. 

4 . A motor whose efficiency is 90 °/o delivers 10 H.P. What must 
be the input ? 

5 . In a system of pulleys a tension of 100 lb. is applied to the 
rope and the rope is drawn 60 ft., while a weight of 500 lb. is lifted 
10 ft. What is the efficiency of the system? 

6 . A weight of 100 lb. is lifted by a lever of the second kind. 
The weight is placed 2 ft. from the fulcrum and the lever is 12 ft. 
long. What force is necessary ? 

7 . A bar 4 m. long is of uniform size and weighs 1 kg. to the meter. 
A weight of 10 kg. is placed at one end, and the fulcrum is 1 m. from 
that end. What weight at the other end will produce a balance ? 

8 . In order to lift a weight of 500 lb. at one end of a bar 15 ft. 
long, a weight of 100 lb. is used at the other end. The bar is of uni¬ 
form size and weighs 25 lb. Where must the fulcrum be placed ? 

9 . The axle on which the rope wound in a windlass was 8 in. in 
diameter. The crank was 12 in. long and the weight lifted was 200 lb. 
What force was applied? 

10. The diameter of a ship’s capstan is 16 in. What force must 
be applied to each of two handspikes at an effective distance of 6 ft. 
to turn the capstan and lift an anchor weighing 2400 lb. if the 
efficiency of the machine is 80 per cent ? 

11 . In a system of six pulleys, three of which are movable, how 
many kilograms can a force of 25 kg. support? 

12. A jackscrew was used to lift a weight of 200 lb. The lever 
was 2 ft. long and the screw had 4 threads to the inch. Assuming an 
efficiency of 100 $>, what force was applied at the end of the handle? 

13 . The radii of a wheel and the axle are 5 ft. and 5 in. respec¬ 
tively. It was found that a force of 100 lb. could lift a weight of 
960 lb. What weight would 100 lb. of force lift if there were no 
friction ? What is the efficiency of the machine? 

14 . If the front sprocket wheel of a bicycle contains 24 sprockets 
and the rear one 8, how far will one complete turn of the pedals drive 
a 28 in. wheel? 


CHAPTER VII 


SOUND 

I. WAVE MOTION 


190. Vibrations. — A vibrating body is one which re¬ 
peats its limited motion at regular short intervals of time. 
A complete or double vibration is the motion between two 
successive passages of the moving body through any point 
of its path in the same direction. 


If we suspend a ball by a long thread and set it swinging like a 
common pendulum, it will return at regular intervals to the starting 
point. If we set the ball moving in a circle, 
the string will describe a conical surface and 
the ball will again return at the same inter¬ 
vals to the starting point. 

191. Kinds of Vibration. —Clamp one 
end of a thin steel strip in a vise (Fig. 172); 
draw the free end aside and release it. It 
will move repeatedly from D' to D" and 
back again. The shorter or thicker the strip, 
the quicker its vibration; when it becomes 
like the prong of a tuning fork, it emits a 
musical sound. 

Vibrations like these are transverse. 
Figure 172 . — Vibration A body vibrates transversely when the 
of Steel Strip. direction of the motion is at right angles 
to its length. The strings of a violin, the reeds of a 
cabinet organ, and the wires of a piano are familiar ex¬ 
amples. 



176 






TRANSVERSE WAVES 


177 


Fasten the ends of a long spiral spring securely to fixed supports 
with the spring slightly stretched. Crowd together a few turns of 
the spiral at one end and 
release them. A vibratory 
movement will travel from 
one end of the spiral to the Figure 173. — Vibratory Motion in Spring. 

other, and each turn of wire will swing backward and forward in the 
direction of the length of the spiral (Fig. 173). 

The vibrations of the spiral are longitudinal. A body 
vibrates longitudinally when its parts move backward and 
forward in the direction of its length. The vibrations set 
up in a long glass tube by stroking it lengthwise with a 
damp cloth are longitudinal; so are those of the air in a 
trumpet and the air in an organ pipe. 

192. Wave Motion. — Tie one end of a soft cotton rope, such 
as a clothesline, to a fixed support; grasp the other end and stretch 
the rope horizontally. Start a disturbance by an up-and-down motion 
of the hand. Each point of the rope will vibrate with simple har¬ 
monic motion (§ 112), while the disturbance will travel along the rope 
toward the fixed end. 

This progressive change of form due to the periodic vibra¬ 
tion of the particles of the medium is a wave. The particles 
are not all in the same phase (§ 112) or stage of vibration, 
but they pass through corresponding positions in suc¬ 
cession. 

193. Transverse Waves. — A small camel’s-hair brush is at¬ 
tached to the end of a long slender strip of clear wood, mounted as 




Figure 174 . — Inscribing Transverse Wave. 

shown in Fig. 174, which was made from a photograph giving an 
oblique view of the apparatus. The brush should touch lightly the 












178 


SOUND 


paper attached to the narrow board, which may be moved in a straight 
line against the guiding strip. Ink the brush and while it is at rest 
push the paper along under it. The brush will mark the straight 
middle line running through the curve shown in the figure. Replace 
the board in the starting position; then pull the strip aside and 
release it. Again draw the board under the brush with uniform 
motion. This time the brush traces the curved line. 

The strip of wood vibrates at right angles to the direc¬ 
tion of motion of the paper with a simple harmonic motion 
(§112); the board moves with a uniform rectilinear 
motion; the curve is a simple harmonic curve. It is the 
resultant of the two motions, and illustrates a transverse 
wave . A transverse wave is one in which the vibration of the 
particles in the wave is at right angles to the direction in 
which the wave is traveling. 


194. To Construct a Transverse Wave. — Suppose a series of 
particles, originally equidistant in a horizontal straight line, to 


9 

t 1 T 

I I 


C J | | , 

fi ll 

sJ- M j 1 I 


i 

T 

I T 

! ! 1 


J-A. 


m il 

l I I 
I l 


A 1 
s 

Figure 175 . — Position of Particles in Wave. 


n 


Vibrate transversely with simple harmonic motion. Let Fig. 175 
represent the position of the particles at some particular instant, the 
displacement of each one from the straight horizontal line being 
found by means of an auxiliary circle as in § 112. They will out¬ 
line a transverse wave. At g the particle has reached its extreme 
displacement in the positive direction and is momentarily at rest; 
the particle at s has reached its maximum negative displacement, and 
is also at rest. The particle at m is moving in the positive direction 










LONGITUDINAL WAVE 


179 


with maximum velocity, and the particles a and y with maximum 
velocity in the negative direction. If the wave is traveling to the 
right, then an instant later the displacement of g will have diminished 
and that of i will have increased to a maximum, the crest having 
moved forward from g to i in the short interval. The successive 
particles of the wave all differ in phase by the same amount. 

195. Longitudinal Wave. — Place a lighted candle at the conical 
end of the long tin tube of Fig. 176. Over the other end stretch a 



Figure 176 . — Wave of Compression in Tube. 


piece of parchment paper. Tap the paper lightly with a cork mallet; 
the transmitted impulse will cause the flame to duck, and it may 
easily be blown out by a sharper blow. 

The air in the tube is agitated by a vibratory motion, 
and a wave, consisting of a compression followed by a 
rarefaction, traverses the tube. The dipping of the flame 
indicates the arrival of the compression. Each particle 
of air vibrates longitudinally in the tube, the disturbance 
being similar to that of the vibrating spiral. 



B d F H 



a c e a 

Figure 177 . — Particles in Wave of Compression. 


Figure 177 illustrates the distribution of the air particles 
when disturbed by such a longitudinal wave of com¬ 
pressions and rarefactions. B, I), F , etc., are regions of 
compressions; A, C, F, etc., those of rarefaction. The 







180 


SOUND 


distances of the different points of the curve from the 
straight line denote the relative velocities of the air 
particles. The greatest velocity forward is at the middle 
of the condensation, as at B , and the greatest velocity 
backward is at the middle of the rarefaction, as at A. 
A and (7, or B and 2), are in the same phase , that is, in 
corresponding positions in their path. 

A longitudinal wave is one in which the vibrations are 
backward and forward in the same direction as the wave is 
traveling . 

196. Wave Length. — The length of a wave is the distance 
from any particle to the next one in the same phase , as 
from a to y (Fig. 175), or from d to 0 or B to I) 
(Fig. 177). Since the wave form travels from a to ?/, or 
from A to (7, during the time of one complete vibration of 
a particle, it follows that the wave length is also the 
distance traversed by the wave during one vibration period. 

197. Water Waves. — One of the most familiar examples of 
transverse waves are those on the surface of water. For deep water 

Figure 178 . — Water Wave. 

the particles describe circles, all in the same vertical plane containing 
the direction in which the wave is traveling, as illustrated in Fig. 178. 
The circles in the diagram are divided into eight equal arcs, and the 
water particles are supposed to describe these circles in the direction 
of watch hands and all at the same rate; but in any two consecutive 
circles their phase of motion differs by one eighth of a period, that is, 
the water particles are taken at such a distance apart that each one 
begins to move just as the preceding one has completed one eighth 
part of its orbit. When a has completed one revolution, b is one 
eighth of a revolution behind it, c two eighths or one quarter, etc. 






SOURCE OF SOUND 


181 


A smooth curve drawn through the positions of the particles in the 
several circles at the same instant is the outline or contour of a wave. 

When a particle is at the crest of a wave, it is moving in the same 
direction as the wave; when it is in the trough, its motion is opposite 
to that of the wave. 

The crests and troughs are not of the same size, and the larger the 
circles (or amplitude), the smaller are the crests hi comparison with 
the troughs. Hence the crests of high waves tend to become sharp or 
looped, and they break into foam or white caps. 

II. SOUND AND ITS TRANSMISSION 

198. Sound may be defined as that form of vibratory mo¬ 
tion in elastic matter which affects the auditory nerves , and 
produces the sensation of hearing. All the external phenom¬ 
ena of sound may be present without any ear to hear. 
Sound should therefore be distinguished from hearing. 

199. Source of Sound. — If we suspend a small elastic ball by a 
'thread so that it just touches the edge of an inverted bell jar, and 

strike the edge of the jar with a felted or cork mallet, the ball will 
be repeatedly thrown away from the jar as long as the 
sound is heard. This shows that the jar is vibrating 
energetically. 

Stretch a piano wire over the table and a little above 
it. Draw a violin bow across the wire, and then touch 
it with the suspended ball of the previous paragraph. 

So long as the wire emits sound the ball will be thrown 
away from it again and again. 

If a mounted tuning fork (Fig. 179) is sounded, and 
a light ball of pith or ivory, suspended by a thread, is 
brought in contact with one of the prongs at the back, 
it will be briskly thrown away by the energetic vibra¬ 
tions of the fork. 

Partly fill a glass goblet with water, and produce a musical note by 
drawing a bow across its edge. The tremors of the glass will throw 
the surface of the water into violent agitation in four sectors, with 
intermediate regions of relative repose. This agitation disappears 
when the sound ceases. 



Figure 179 . 
—Vibration of 
Tuning Fork. 





182 


SOUND 


A glass tube, four or five feet long, may be made to emit a musical 
sound by grasping it by the middle and briskly rubbing one end with 
a cloth moistened with water. The vibrations are longitudinal, and 
may be so energetic as to break the tube into many narrow rings. 

Experiments like these show that the sources of sound 
are bodies in a state of vibration. Sound and vibratory 
movement are so related that one is strong when the other 
is strong, and they diminish and cease together. 


200. Media for Transmitting Sound. — Suspend a small electric 
bell in a bell jar on the air pump table (Fig. 180). When the air 

is exhausted, the bell is nearly inau¬ 
dible. Sound does not travel through 
a vacuum. 

Fasten the stem of a tuning fork to 
the middle of a thin disk of wood. 
Set the fork vibrating, and hold it with 
the disk resting on the surface of water 
in a tumbler, standing on a table. 
The sound, which is scarcely audible 
when there is no disk attached to the 
fork, is now distinctly heard as if coming from the table. 

Hold one end of a long, slender wooden rod against a door, and rest 
the stem of a vibrating fork against the other end. The sound will be 
greatly intensified, and will come from the door as the apparent source. 

Press down on a table a handful of putty or dough, and insert in it 
the stem of a vibrating fork; the vibrations will not be conveyed to 
the table to an appreciable extent. 



Figure 180. — Bell in Vacuum. 


Only elastic matter transmits sound, and some kinds 
transmit it better than others. 

201. Transmission of Sound to the Ear. — Any uninter¬ 
rupted series of elastic bodies will transmit sound to the 
ear, be they solid, liquid, or gaseous. 

A bell struck under water sounds painfully loud if the ear of the 
listener is also under water. A diver under water can hear voices in 
the air. By placing the ear against the steel rail of a railway, two 
sounds may be heard, if the rail is struck some distance away: a 






Lord Rayleigh (John William Strutt) was born at Essex in 
1842, and graduated from Cambridge University in 1865. In 
1884 he was appointed professor of experimental physics in that 
institution, and three years later he was elected professor of natu¬ 
ral philosophy at the Royal Institution of Great Britain. His work 
is remarkable for its extreme accuracy. The discovery of argon 
in the atmosphere, while attempting to determine the density of 
nitrogen, was the result of a very minute difference between the 
result obtained by using nitrogen from the air and that from 
another source. Nearly every department of physics has been 
enriched by his genius. His treatise on Sound is one of the finest 
pieces of scientific writing ever produced. His determination of 
the electrochemical equivalent of silver and the electromotive 
force of the Clark standard cell are important contributions to 
modern electrical measurements. He died in 1919. 



Photographs of Sound-Waves produced by an Electric Spark behind a 

Black Disk. 

(Taken by Professor Foley of Indiana University .) 



1. A spherical sound-wave. 

2. The same wave a fraction of a second later. 

3. Spherical sound-wave reflected from a plate of plane glass. 

4. The same wave a moment later. The broken line near the black disk 

shows the effect of the puff of hot air from the spark. 

5. Sound-wave reflected from a parabolic reflector. The source is at the 

focus and the reflected wave is plane. 

6. The same wave a moment later, showing its central portion advanced 

by the puff of hot air from the spark. 






























MOTION OF THE PARTICLES OF A WAVE 183 


louder one through the rails and then another through the air. The 
faint scratching of a pin on the end of a long stick of timber, or the 
ticking of a watch held against it, may be heard very distinctly if the 
ear is applied to the other end. 

The earth conducts sound so well that the stepping of a horse may 
be heard by applying the ear to the ground. This is understood by 
the Indians. The firing of a cannon at least 200 miles away may be 
heard in the same way. The report of a mine blast reaches a listener 
sooner through the earth than through the air. 

The great eruption of Krakatoa in 1883 gave rise to gigantic 
sound waves, which produced at a distance of 2000 miles a report 
like the firing of heavy guns. 

202. Sound Waves. *— When a tuning fork or similar 
body is set vibrating, the disturbances produced in the 
air about it are known as sound waves. They consist of a 
series of condensations and rarefactions succeeding each 
other at regular intervals. Each particle of air vibrates 
in a short path in the direction of the sound transmission. 
Its vibrations are longitudinal as distinguished from the 
transverse vibrations in water waves. 

203. Motion of the Particles of a Wave. — The motion of 
the particles of the medium conveying sound is distinct 
from the motion of the sound wave. A sound wave is 
composed of a condensation followed by a rarefaction. 
In the former the particles have a forward motion in the 
direction in which the sound is traveling; in the latter 
they have a backward motion, while at the same time both 
condensation and rarefaction travel steadily forward. 

The independence of the two motions is aptly illustrated by a field of 
grain across which waves elcited by the wind are coursing. Each stalk 
of grain is securely anchored to the ground, while the wave sweeps 
onward. The heads of grain in front of the crest are rising, while all 
those behind the crest and extending to the bottom of the trough are 
falling. They all sweep forward and backward, not simultaneously , 
but in succession , while the wave itself travels continuously forward. 


184 


SOUND 



III. VELOCITY OF SOUND 

204. Velocity in Air. — In 1822 a scientific commission 
in France made experiments to ascertain the velocity of 
sound in air. Their method was to divide into two par¬ 
ties at stations a measured distance apart, and to determine 
the interval between the observed flash and the report of 


View of Lake Geneva. 

a cannon fired alternately at the two stations. The mean 
of an even number of measurements eliminated very nearly 
the effect of the wind. The final result was 831 m. per 
second at 0° C. The defect of the method is that the per¬ 
ception of sound and of light are not equally quick, and 
they vary with different persons. 

Subsequent observers, employing improved methods, 
and correcting for all sources of error, have obtained as 
the most probable velocity 332.4 m., or 1090.5 ft., per 
second at 0° C. At higher temperatures sound travels 







QUESTIONS AND PROBLEMS 


185 


faster, the correction being 0.6 m., or nearly 2 ft., per de¬ 
gree Centigrade. At 20° C. (68° F.) the velocity is very 
nearly 1180 ft. per second. 

205. Velocity in Water. — In 1827 Colladon and Sturm, 
by a series of measurements in Lake Geneva, found that 
sound travels in water at the rate of 1435 m. per second at 
a mean temperature of 8.1° C. They measured with 
much care the time required for the sound of a bell struck 
under water to travel through the lake between two boats 
anchored at a distance apart of 13,487 m. It was 9.4 sec¬ 
onds. 

A system of transmitting signals through water by means of sub¬ 
merged bells is in use by vessels at sea and for offshore stations. Spe¬ 
cial telephone receivers have been devised to operate under water and 
to respond to these sound signals. Indeed, the vessel itself acts as a 
sounding board and as a very good receiver. 

206. Velocity in Solids. — The velocity of sound in solids 
is in general greater than in liquids on account of their 
high elasticity as compared with their density. The ve¬ 
locity in iron is 5127 m. per second; in glass 5026 m. per 
second ; but' in lead it is only 1228 m. per second, at a 
temperature in each case of 0° C. 

Questions and Problems 

1. Why do the timers in a 200-yd. dash start their stopwatches by 
the flash of the pistol rather than by the report? 

2. If the flash of a gun is seen 3 sec. before the report is heard, 
how far is the gun from the observer, the temperature being 20° C. ? 

3. The interval between seeing a flash of lightning and hearing 
the thunder was 5 sec.; the temperature was 25° C. How far away 
was the lightning discharge ? 

4 . Signals given by a gun 2 mi. away would be how much in 
error when the temperature is 20° C. and the wind is blowing 10 mi. 
an hour in the direction from the listener to the gun ? 


186 


SOUND 


5. A man sets his watch by a steam whistle which blows at 12 
o’clock. The whistle is 1.5 mi. away and the temperature 15° C. 
How many seconds will the watch be in error ? 

6. A ball fired at a target was heard to strike after an interval of 
8 sec. The distance of the target was 1 mi. and the temperature of 
the air 20° C. What was the mean velocity of the ball ? 

7. The distance between two points on a straight stretch of rail¬ 
way is 2565 m. An observer listens at one of these points and a 
blow is struck on the rails at the other. If the temperature is 0° C., 
what is the interval between the arrival of the two sounds, one 
through the rails and the other through the air? 

8. A man watching for the report of a signal gun saw the flash 
2 sec. before he heard the report. If the temperature was 0° C. and 
the distance of the signal gun was 2225 ft., what was the velocity of 
the wind ? 

9. A shell fired at a target, distance half a mile, was heard to 
strike it 5 sec. after leaving the gun. What was the average speed 
of the bullet, the temperature of the air being 20° C. ? 

IV. REFLECTION OF SOUND 

207. Echoes. —An echo is the repetition of a sound by re - 
flection from some distant surface. A clear echo requires 
a vertical reflecting surface, the dimensions of which are 
large compared to the wave length of the sound. A cliff, 
a wooded hill, or the broad side of a large building may 
serve as the reflecting surface. Its inequalities must be 
small compared to the length of the incident sound waves ; 
otherwise, the sound is diffused in all directions. 

A loud sound in front of a tall cliff an eighth of a mile 
away will be returned distinctly after about a second and 
a sixth. If the reflecting surface is nearer than about fifty 
feet, the reflected sound tends to strengthen the original 
one, as illustrated by the greater distinctness of sounds 
indoors than in the open air. In large rooms where the 
echoes produce a confusion of sounds the trouble may be 





Echo Bridge over the Charles near Boston. 

A shout under this bridge reverberates from the bridge to the water and back over and over again. 







































































































































































. 

























































































■ 


















































































































































































AERIAL ECHOES 


187 



m mm i > 

-jy ! -' ■'" ! 1 i 

i^‘^ e ii hmiiIih ii a...tn inii* ■■-• -A ii i * 


diminished by adopting some method to prevent regular 
reflection, such as the hanging of draperies, or covering 
the walls with absorbing materials. 

208. Multiple Echoes. —Parallel reflecting surfaces at a 
suitable distance produce multiple echoes , as parallel mir¬ 
rors produce multiple 
images (§ 261). The 
circular baptistery at 
Pisa and its spherical 
dome' prolong a sound 
for ten or more seconds 
by * successive reflec¬ 
tions; the effect is made 
more conspicuous by the 
good reflecting surface 
of polished marble. Ex¬ 
traordinary echoes some¬ 
times occur between the 
parallel walls of deep 
canons. 

209. Aerial Echoes. — 

Whenever the medium 
transmitting sound changes suddenly in density, a part of 
the energy is transmitted and a part reflected. The in¬ 
tensity of the reflected system is the greater the greater 
the difference in the densities of the two media. A dry 
sail reflects a part of the sound and transmits a part; 
when wet it becomes a better reflector and is almost im¬ 
pervious to sound. 

Aerial echoes are accounted for by sudden changes of 
density in the air. Air, almost perfectly transparent to 
light, may be very opaque to sound. When for any rea¬ 
son the atmosphere becomes unstable, vertical currents 


The Baptistery at Pisa. 







188 


SOUND 


and vertical banks of air of different densities are formed. 
The sound transmitted by one bank is in part reflected by 
the next, the successive reflections giving rise to a curious 
prolonging of a short sound. Thus, the sound of a gun 
or of a whistle is then heard apparently rolling away to a 
great distance with decreasing loudness. 


210. Whispering Gallery. — Let a watch be hung a few inches 
in front of a large concave reflector (Fig. 181). A place may be found 

for the ear at some distance in 
front, as at E, where the ticking of 
the watch may be heard with great 
distinctness. The sound waves, 
after reflection from the concave 
surface, converge to a point at E. 

The action of the ear trumpet 
depends on the reflection of sound 
from curved surfaces; the sides of 
the bell-shaped mouth reflect the sound into the tube which conveys 
it to the ear. 



Figure 181. — Reflector 
Sound. 


An interesting case of the reflection of sound occurs in 
the whispering gallery , where a faint sound produced at 
one point of a very large room is distinctly heard at some 
distant point, but is inaudible at points between. It re¬ 
quires curved walls which act as reflectors to concentrate 
the waves at a point. Low whispers on one side of the 
dome of St. Paul’s in London (see page 81) are distinctly 
audible on the opposite side. 


V. RESONANCE 

211. Forced Vibrations. —A body is often compelled to 
surrender its natural period of vibration, and to vibrate 
with more or less accuracy in a manner imposed on it by 
an external periodic force. Its vibrations are then said 
to be forced. 



SYMPATHETIC VIBRATIONS 


189 


Huyghens discovered that two clocks, adjusted to slightly differ' 
ent rates, kept time together when they stood on the same shelf. 
The two prongs of a tuning fork, with slightly different natural 
periods on account of unavoidable differences, mutually compel each 
other to adopt a common frequency. These two cases are examples 
of mutual control, and the vibrations of both members of each pair 
are forced. 

The sounding board of a piano and the membrane of a banjo are 
forced into vibration by the strings stretched over them. The top 
of a wooden table may be forced into vibration by pressing against 
it the stem of a vibrating tuning fork. The vibrations of the table 
are forced and it will respond to a fork of any period. 

212. Sympathetic Vibrations. — Place two mounted tuning 
forks, tuned to exact unison, near each other on a table. Keep one 
of them in vibration for a few seconds and then stop it; the other 
one will be heard to sound. 

In the case of these forks, the pulses in the air reach 
the second fork at intervals corresponding to its natural 
vibration period and the effect is' cumulative. The ex¬ 
periment illustrates sympathetic vibrations in bodies hav¬ 
ing the same natural period. If the forks differ in period, 
the impulses from the first do not produce cumulative 
effects on the second, and it will fail to respond. 

♦ 

Suspend a heavy weight by a rope and tie to it a thread. The 
weight may be set swinging by pulling gently on the thread, releas¬ 
ing it, and pulling again repeatedly when the weight is moving in 
the direction of the pull. 

Suspend two heavy pendulums on knife-edges on the same stand, 
and carefully adjust them to swing in the same period. If then one 
is set swinging, it will cause the other one to swing, and will give up 
to it nearly all its own motion. 

When the wires of a piano are released by pressing the loud pedal, 
a note sung near it will be echoed by the wire which gives a tone of 
the same pitch. 

A number of years ago a suspension bridge of Manchester in Eng¬ 
land was destroyed by its vibrations reaching an amplitude beyond 


190 


SOUND 


the limit of safety. The cause was the regular tread of troops keep¬ 
ing time with what proved to be the natural rate of vibration of the 

bridge. Since then the custom has 
always been observed of breaking 
step when bodies of troops cross a 
bridge. 

213. Resonance. — Reso¬ 
nance is the reenforcement of 
sound by the union of direct 
and reflected sound waves. 

Hold a vibrating tuning fork 
over the mouth of a cylindrical jar 
(Fig. 182). Change the length of 
the air column by pouring in water 
slowly. The sound will increase in 
loudness until a certain length is 
reached, after which it becomes 
weaker. A fork of different pitch 
F.oure 182. -^enforcement of wiU require a diflerent length of 

air column to reenforce its sound. 

The “ sound of the sea ” heard when a sea shell is held to the ear 
is a case of resonance. The mass of air in the shell has a vibration 
rate of its own, and it amplifies any 
faint sound of the same period. A 
vase with a long neck, or even a tea¬ 
cup, will also exhibit resonance. 

The box on which a tuning fork 
is mounted (Fig. 183) is a resonator, 
designed to increase the volume of 
sound. The air within the body of 
a violin and all instruments of like 
character acts as a resonator. The 
air in the mouth, the larynx, and 
the nasal passages is a resonator; the Figure 183. — Mounted Tuning 
length and volume of this body of air Fork. 

can be changed at pleasure so as to reenforce sounds of different 
pitch. 














PITCH 


191 


214. The Helmholtz Resonator. — The resonator devised by 


Helmholtz is spherical in form, 
sides (Fig. 184). The larger 
opening A is the mouth of the 
resonator; the smaller one B fits 
in the ear. These resonators are 
made of thin brass or of glass, 
and their pitch is determined by 
their size. When one of them 
is held to the ear, it strongly 
reenforces any sound of its own 
rate of vibration, but is silent to 
others. 


with two short tubes on opposite 



Figure 184. — Helmholtz Resonator. 


VI. CHARACTERISTICS OF MUSICAL SOUNDS 


215. Musical Sounds. — Sounds are said to be musical 
when they are pleasant to the ear. They are caused by 
regular periodic vibrations. A noise is a disagreeable 
sound, either because the vibrations producing it are not 
periodic, or because it is a mixture of dis¬ 
cordant elements, like the clapping of the 
hands. 

Musical sounds have three distinguish¬ 
ing characteristics: pitch , loudness, and 
quality. 



216. Pitch. — Mount on the axle of a whirling 
machine (Fig. 185), or on the armature of a small 
electric motor, a cardboard or metal disk D with 
a series of equidistant holes in a circle near its 
edge. While the disk is rotating rapidly, blow a 
stream of air through a small tube against the 
circle of holes. A distinct musical tone will be 
produced. If the experiment be repeated with the 
disk rotating more slowly, or with a circle of a 
smaller number of holes, the tone will be lower; if the disk is rotated 
more rapidly, the tone will be higher. 


Figure 185. —• 
Siren. 





192 


SOUND 


The air passes through the holes in a succession of puffs producing 
waves in the air. These waves follow one another with definite 
rapidity, giving rise to the characteristic of sound called pitch. We 
conclude that the pitch of a musical sound depends only upon the number 
of pulses which reach the ear per second. To Galileo belongs the credit 
of first pointing out the relation of pitch to frequency of vibration. 
He illustrated it by drawing the edge of a card over the milled edge 
of a coin. 

217. Relation between Pitch, Wave Length, and Velocity.— 

If a tuning fork makes 256 vibrations per second, and 
in that time a sound travels in air, at 20° C., a distance of 
344 m., then the first wave will be 344 m. from the fork 
when it completes its 256th vibration. Hence, in 344 m., 
there will be 256 waves, and the length of each will be 
m., or 1.344 m. In general, then, 

wave length = . , 

frequency 


or in symbols, l — -, v = nl, and n = 


(Equation 31) 


218. Loudness. —The loudness of a sound depends on 
the intensity of the vibrations transmitted to the ear. 
The energy of the vibrations is proportional to the square 
of their amplitude ; but since it is obviously impracticable 
to express a sensation in terms of a mathematical formula, 
it is sufficient to say that the loudness of a sound increases 
with the amplitude of vibration. 

As regards distance, geometrical considerations would 
go to show that the energy of sound waves in the open 
decreases as the square of the distance increases, but the 
actual decrease in the intensity of sound is even greater 
than this. The energy of sound waves is gradually dis¬ 
sipated by conversion into heat through friction and 
viscosity. 









Hermann von Helmholtz (1821-1894) was born at Potsdam. 
He received a medical education at Berlin and planned to be a 
specialist in diseases of the eye, ear, and throat. His studies soon 
revealed to him the need of a knowledge of physics and mathe¬ 
matics. To these subjects he gave his earnest attention and soon 
became one of the greatest physicists and mathematicians of the 
nineteenth century. He made important contributions to all de¬ 
partments of physical science. He is the author of an important 
work on acoustics and is celebrated for his discoveries in this 
field. But perhaps his most useful contribution is that of the 
ophthalmoscope, an instrument of inestimable value to the oculist 
in examining the interior of the eye. 






QUALITY 


193 


The area of the vibrating body affects the loudness. 
This is illustrated in the piano, where strings of different 
diameters produce sounds differing in loudness. The 
thicker vibrating string sets more air in motion, and the 
wave has in consequence more energy. 

The less dense the medium in which the vibration is set 
up, the feebler the sound. On a mountain top the report 
of a gun is comparable in loudness with that produced by 
the breaking of a stick at the base. The electric bell in a 
partially exhausted receiver (§ 200) is nearly inaudible. 

Fill three large battery jars with coal gas, air, and carbonic acid 
respectively. Ring in them successively a small bell. There will be 
a marked difference in loudness. 

219. Quality. —Two notes of the same pitch and loud¬ 
ness, such as those of a piano and a violin, are yet clearly 
distinguishable by the ear. This distinction is expressed 
by the term quality or timbre. Helmholtz demonstrated 
that the quality of a note is determined by the presence of 
tones of higher pitch, whose frequencies are simple mul¬ 
tiples of that of the fundamental or lowest tone. These 
are known as overtones. 

The quality of sounds differs because of the series of 
overtones present in each case. Voices differ for this 
reason. Violins differ in sweetness of tone because the 
sounding boards of some bring out overtones different 
from those of others. Even the untrained ear can readily 
appreciate differences in the character of the music pro¬ 
duced by a flute and a cornet. Voice culture consists in 
training and developing the vocal organs and resonance 
cavities, to the end that purer overtones may be secured, 
and greater richness may by this means be imparted to 
the voice. 


194 


SOUND 


VII. INTERFERENCE AND BEATS 

220. Interference. — Hold a vibrating tuning fork over a cylin¬ 
drical jar adjusted as a resonator, and turn the fork on its axis until 

a position of minimum 
loudness is found. In this 
position cover one prong 
with a pasteboard tube 
without touching (Fig. 
186). The sound will be 
restored to nearly maxi¬ 
mum loudness, because 
the paper cylinder cuts off 
the set of waves from the 
covered prong. 

It is well known 
that the loudness of 
the sound of a vibrat¬ 
ing fork held freely 
in the hand near the 
ear, and turned on its 
In four positions the 
sound is nearly inaudible. Let A , B (Fig. 187) be the 
ends of the two prongs. They vibrate with the same fre¬ 
quency, but in opposite direc¬ 
tions, as indicated by the arrows. 

When the two approach each 
other, a condensation is pro¬ 
duced. between them, and at the 
same time rarefactions start 
from the backs at c and d. The 
condensations and rarefactions 
meet along the dotted lines of 
equilibrium, where partial ex¬ 
tinction occurs, because a rare- 



Figure 187. — Interference 
from Prongs of Tuning Fork. 



Figure 186 . — Interference. 
stem, exhibits marked variations. 













BEATS 


195 


faction nearly annuls a condensation. When the fork is 
held over the resonance jar so that one of these lines of 
interference runs into the jar, the paper cylinder cuts off 
one set of waves, and leaves the other to be reenforced by 
the air in the jar. 

Interference is the superposition of two similar sets of 
waves traversing the medium at the same time . One of 
the two sets of similar waves may be direct and the other 
reflected. If two sets of sound waves of equal length and 
amplitude meet in opposite phases, the condensation of one 
corresponding with the rarefaction of the other, the sound 
at the place of meeting is extinguished by interference. 

221. Beats. — Place near each other two large tuning forks of 
the same pitch and mounted on resonance boxes. When both are set 
vibrating, the sound is smooth, as if only one fork were sounding. 
Stick a small piece of wax to a prong of one fork: this load increases 
its periodic time of vibration, and 
the sound given by the two is now 
pulsating or throbbing. 

Mount two organ pipes of the same 
pitch on a bellows, and sound them 
together. If they are open pipes, a 
card gradually slipped over the open 
end of one of them will change its 
pitch enough to bring out strong 
pulsations. 

With glass tubes and jet tubes set 
up the apparatus of Fig. 188. One 
tube is fitted with a paper slider so 
that its length may be varied. Wh en 
the gas flame is turned down to the 
proper size, the tube gives a continu¬ 
ous sound known as a “singing 
flame.” By making the tubes the 
same length, they may be made to yield the same note, the com¬ 
bined sound being smooth and steady. Now change the position 



Figure 188. — Interference with 
Singing Flames. 








19b 


SOUND 


of the slider, and the sound will throb and pulsate in a disagreeable 
manner. 

These experiments illustrate the interference of two sets 
of sound waves of slightly different period. The outbursts 
of sound , followed by short intervals of comparative silence , 
are called beats. 

Figure 189 illustrates the composition of two transverse 
waves of slightly different length. The addition of the 



Figure 189 . — Interference of Two Transverse Waves. 


ordinates of the two waves ABO gives the wave A!B'0\ 
with a minimum amplitude at B ! . 

222. Number of Beats. — If two sounds are produced by 
forks, for example, making 100 and 110 vibrations per 
second respectively, then in each second the latter fork 
gains ten vibrations on the former. There must be ten 
times during each second when they are vibrating in the 
same phase, and ten times in opposite phase. Hence, in¬ 
terference of sound must occur ten times a second, and 
ten beats are produced. Therefore, the number of beats 
per second is equal .to the difference of the vibration rates 
(, frequencies ) of the two sounds. 

VIII. MUSICAL SCALES 

223. Musical Intervals. — A musical interval is the rela¬ 
tion between two notes expressed as the ratio of their 
frequencies of vibration. Many of these intervals have 


TEE MAJOR DIATONIC SCALE 


197 


names in music. When the ratio is 1 , the interval is 
called unison; 2, an octave; §, a fifth; f, a fourth; etc. 
Any three notes whose frequencies are as 4:5:6 form a 
major triad , and alone or together with the octave of the 
lowest note, a major chord. Any three notes whose fre¬ 
quencies are as 10 : 12 : 15 form a minor triad , and alone or 
with the octave of the lowest, a minor chord. 

Mount the disk of Fig. 190 on the whirling table of Fig. 185. The 
disk is perforated with four circles of equidistant holes, numbering 
24, 30, 36, and 48 respectively. These are 
in the relation of 4, 5, 6, 8. Rotate with 
uniform speed, and beginning with the 
inner circle, blow a stream of air against 
each row of holes in succession. The 
tones produced will be recognized as do, 
mi, sol, do', forming a major chord. If 
now the speed of rotation be increased, 
each note will rise in pitch, but the musical 
sequence will remain the same. 

It will be seen from the fore- Figure 19 °- DlSK for 
. ,. . Major Chord. 

going relations that harmonious 

musical intervals consist of very simple vibration ratios. 

224. The Major Diatonic Scale. — A musical scale is a 
succession of notes by which musical composition ascends 
from one note, called the keynote , to its octave. This last 
note in one scale is regarded as the keynote of another 
series of eight notes with the same succession of intervals. 
In this way the series is extended until the limit of pitch 
established in music is reached. 

The common succession of eight notes, called the major 
diatonic scale , was adopted about three hundred and fifty 
years ago. The octave beginning with middle O is written 

<?' d 1 e 1 f g 1 a’ V c n 




198 


SOUND 


The three major triads for the keynote of C are: 


c' : 

: e' 

: 9' 

9' : 

: V : 

: d" 

f s 

: a’ 

: c" 


The frequency universally assigned to c r in physics is 
256. It is convenient because it is a power of 2, and it 
is practically that of the “middle C ” of the piano If c r 
is due to 256, or ra, vibrations per second, the frequency 
of the other notes of the diatonic scale may be found by 


proportion from the 
follows: 

three 

triads 

above; 

they 

are 

256 

288 

320 

341* 

/' 

384 

426f 

a r 

480 

512 

c } 

d' 

e 1 

• 9’ 

V 

c" 

do 

re 

mi 

/« 

sol 

la 

si 

do 

m 


| m 

f m 

I TO 

| TO 

TO 

2 m 


If the fractions representing the relative frequencies be 
reduced to a common denominator, the numerators may 
be taken to denote the relative frequencies of the eight 
notes of the scale. They are 

24 27 30 32 36 40 45 48 

An examination of these numbers will show that there 
are only three intervals from any note to the next higher. 
They are -|, a major tone; a minor tone; and a 
half tone. The order is -|, |, -!g 0 -, |, . 

225. The Tempered Scale. — If C were always the key¬ 
note, the diatonic scale would be sufficient for all purposes 
except for minor chords ; but if some other note be chosen 
for the keynote, in order to maintain the same order of 
intervals, new and intermediate notes will have to be in¬ 
troduced. For example, let D be chosen for the key- 


LIMITS OF PITCH 


199 


note, then the next note will be 288 x f = 324 vibrations, 
a number differing slightly from U. Again, 324 x 
= 360, a note differing widely from any note in the series. 
In like manner, if other notes are taken as keynotes, and 
a scale is built up with the order of intervals of the dia¬ 
tonic scale, many more new notes will be needed. This 
interpolation of notes for both the major and minor scales 
would increase the number in the octave to seventy-two. 

In instruments with fixed keys such a number is un¬ 
manageable, and it becomes necessary to reduce the num- 
ber by changing the value of the intervals. Such a modi¬ 
fication of the notes is called tempering . Of the several 
methods proposed by musicians, that of equal temperament 
is the one generally adopted. It makes all the intervals 
from note to note equal, interpolates one note in each 
whole tone of the diatonic scale, and thus reduces the 
number of intervals in 
the octave to twelve. 

The only accurately 
tuned interval in this 
scale is the octave ; all 
the others are more or 
less modified. The fol ¬ 
lowing table shows the 
differences between the diatonic and the equally tempered 
scales : 

c' d f e' /' g' a ' b' c" 

Diatonic . . . 256 288 320 341.3 384 426.7 480 512 

Tempered. . .256 287.3 322.5 341.7 383.6 430.5 483.3 512 


ra;~. .. „ Ejjg 



—^_ I _ 

1 

—-1— 

1 

1 1 

1 ! 

i u 


C' I df | e' 

s> 

a 

j 


Figure 191. — Scale of C. 


Figure 191 illustrates the scale of O on the staff and the 
keyboard. 

226. Limits of Pitch. — The international pitch , now in 
general use in Europe and America, assigns to a' the vi- 














200 


SOUND 


bration frequency of 435. But some orchestras have 
adopted 440 vibrations for a'. In the modern piano of 
seven octaves the bass A has a frequency of about 27.5, 
the highest A, 3480. The lowest note of the organ is the 
C of 16 vibrations per second; the highest note is the 
same as the highest note of the piano, the third octave 
above a', with a frequency of 3480. 

The limits of hearing far exceed those of music. The 
range of audible sounds is about eleven octaves, or from 
the Q of 16 vibrations to that of 32,768, though many 
persons of good hearing perceive nothing above a fre¬ 
quency of 16,384, an octave lower. 

Questions- and Problems 

1. Why is the pitch of the sounds given by a phonograph raised by 
increasing the speed of the cylinder or the disk containing the record ? 

2. A megaphone or a speaking tube makes a sound louder at a 
distance. Explain why. 

3. The teeth of a circular saw give a note of high pitch when 
they first strike a plank. Why does the pitch fall when the plank is 
pushed further against the saw? 

4. Miners entombed by a fall of rock or by an explosion have 
signaled by taps on a pipe or by pounding on the rock. How does 
the sound reach the surface ? 

5. Two Rookwood vases in the form of pitchers with slender 
necks give musical sounds when one blows across their mouth. Why 
does the larger one give a note of lower pitch than the smaller ? 

6. What note is made by three times as many vibrations as c’ 
(middle C) ? 

7. If c' is due to 256 vibrations per second, what is the frequency 
of g" in the next octave ? 

8. What is the wave length of g’ when sound travels 1130 feet 
per second? 

9. If c' has 264 vibrations per second, how many has a' ? 

10 . When sound travels 1120 ft. per second, the wave length of the 
note given by a fork was 3.5 ft. What was the pitch of the fork? 


LAWS OF STRINGS 


201 


IX. VIBRATION OF STRINGS 

227. Manner of Vibration. — When strings are used to 
produce sound, they are fastened at their ends, stretched 
to the proper tension, and are made to vibrate transversely 
by drawing a bow across them, striking with a light ham¬ 
mer as in the piano, or plucking with the fingers as in the 
banjo, guitar, or harp. 

228. The Sonometer. — The sonometer is an instrument 
for the study of the laws governing the vibration of 



Figure 192. — Sonometer. 


strings. It consists of a thin wooden box, across which are 
stretched violin strings or thin piano wires (Fig. 192). 
The wires pass over fixed bridges, A and B , near the ends, 
and are stretched by tension balances at one end. They 
may be shortened by movable bridges (7, sliding along 
scales under the wires. 

229. Laws of Strings. — Stretch two similar wires on the so¬ 
nometer and tune to unison by varying the tension. Shorten one of 
them by moving the bridge C to f, f, £, f, etc. The successive inter¬ 
vals between the notes given by the two wires will be f, £, f, f, etc. 
The notes given by the wire of variable length are those of the major 
diatonic scale. Hence, 

The frequency of vibration for a given tension varies 
inversely as the length. 

Starting with a given tension and the strings or wires in unison, 
increase the stretching force on one of them four times; it will now 
give the octave of the other with twice the frequency. Increase the 










202 


SOUND 


tension nine times; it will give the octave plus the fifth, or the twelfth, 
above the other with three times the frequency. These statements 
may be verified by dividing the comparison wire by a bridge into 
halves and thirds, so as to put it in unison with the wire of variable 
tension. Hence, 

When the length is constant, the frequency varies as 
the square root of the tension. 

Stretch equally two wires differing in diameter and material, that 
is, in mass per unit length. Bring them to unison with the movable 
bridge. The ratio of their lengths will be inversely as that of the 
square roots of the masses per unit length. Hence, 

The length and tension being constant, the frequency 
varies inversely as the square root of the mass -per unit 
length. 


230. Applications. — In the piano, violin, harp, and other 
stringed instruments, the pitch of each string is determined 
partly by its length, partly by its tension, and partly by 
its size or the mass of fine wire wrapped around it. The 
tuning is done by varying the tension. 


231. Fundamental Tone. — Fasten one end of a silk cord about 
a meter long to one prong of a large tuning fork, and wrap the other 

end around a wooden pin in¬ 
serted in an upright bar in 
such a way th&„ tension can 
be applied to the cord by 
turning the pin. Set the 
fork vibrating, and adjust 
the tension until the cord 
vibrates as a whole (Fig. 
193). Arranged in this way, the frequency of the fork is double that 
of the cord. 



Figure 193. — Fundamental of a String. 


The experiment shows the way a string or wire vibrates 
when giving its lowest or fundamental tone. A body 







NODES AND SEGMENTS 


203 


yields its fundamental tone when vibrating as a whole, or 
in the smallest number of segments possible 


232. Nodes and Segments. —With a silk cord about 2 m. long, 
and mounted as in the last experiment, adjust the tension until the 
cord vibrates in a number of 


giving the appearance 
of a succession of spindles of 
equal length (Fig. 194). The 
frequency of the fork is twice 
that of each spindle. 

Stretch a wire on a sonom¬ 
eter with a thin slip of cork 
strung on it. Place the cork at one third, one fourth, one fifth, or one 
sixth part of the wire from one end; touch it lightly, and bow the 


Figure 194. 


String Vibrating in Seg¬ 
ments. 


shorter portion of the wire. The wire will vibrate in equal segments 
(Fig. 195). The division into segments may be made more conspicu¬ 
ous by placing on the wire, before bowing it, narrow V-shaped pieces 
of paper, or riders. If, for example, the cork is placed at one fourth 



Figure 195. — Wire Vibrating in Segments. 


the length of the wire, the paper riders should be in the middle, and at 
one fourth the length from the other end, and at points midway be¬ 
tween these. When the wire is deftly bowed, the riders at the fourths 
will remain seated, and the intermediate ones will be thrown off. 
The latter mark points of maximum, and the former those of mini¬ 
mum vibration. 

The ends of a wire and the intermediate points of least 
motion are called nodes; the vibrating portions between 






204 


SOUND 


the nodes are loops or segments; and the middle points of 
the loops are called antinodes. The last two experiments 
illustrate what are known as stationary waves. They 
result from the interference of the direct system of waves 
and those reflected from the fixed end of the wire. At 
the nodes the two meet in opposite phase; at the anti¬ 
nodes in the same phase. At the former the motion is re¬ 
duced to a minimum ; at the latter it rises to a maximum. 


233. Overtones in Strings. — Stretch two similar wires on the 
sonometer and tune to unison ; then place a movable bridge at the 

middle of one of them. Set the 
longer wire in vibration by pluck¬ 
ing or bowing it near one end. 
The tone most distinctly heard is 
its fundamental. Touch the wire 


Figure 196. — Fundamental and Oc¬ 
tave Together. 


lightly at its middle point; instead of stopping the sound, a tone is now 
heard in unison with that given by the shorter wire, that is, an octave 
higher than the fundamental and caused by the longer wire vibrating 
in halves (Fig. 196). If the wire be again plucked, both the funda¬ 
mental and the octave may be 
heard together. 

Touching the wire one third 
from the end brings out a tone in 
unison with that given by the 


Figure 197. — Fundamental and Oc¬ 
tave Plus Fifth Together. 


second wire reduced to one third its length by the movable bridge, 
that is, it yields a tone of three times the frequency, or an octave and 
a fifth higher than the fundamental. Figure 197 illustrates the man¬ 
ner in which the wire is vibrating. 


The experiment shows that a wire may vibrate not only 
as a whole but at the same time in parts, yielding a com¬ 
plex note. The tones produced by a body vibrating in 
parts are called overtones or partial tones. 

234. Harmonics. — If the frequency of vibration of the 
overtone is an exact multiple of the fundamental, it is 
called an harmonic partial or simply an harmonic . In 






AIR AS A SOURCE OF SOUND 


205 


strings the overtones are usually harmonics, but in vibrat¬ 
ing plates and membranes they are not. 

The harmonics are named first, second, third, etc., in 
the order of their vibration frequency. The frequency of 
any particular harmonic is found by multiplying that of 
the fundamental by a number one greater than the number 
of the harmonic. For example, the frequency of the first 
harmonic of c 1 of 256 vibrations per second is 256 x 2 = 
512; that of the second is 256 x 3 = 768, etc. 


X. VIBRATION OF AIR IN PIPES 

235. Air as a Source of Sound.—In the use of the res¬ 
onator we saw that air may be thrown into vibration when 



Figure 198 . — Clarinet. 


it is confined in tubes or globes, and that it thus becomes 
the source of sound. Such a body of air may be set 



Figure 199 . — Flute. 


vibrating in two ways; by a vibrating tongue or reed, 
as in the clarinet (Fig. 198), the fish horn, etc., or by a 



Figure 200 . — Trombone. 


stream of air striking against the edge of an opening in 
the tube, as in the whistle, the flute (Fig. 199), the organ 
pipe, etc. In several pipe or wind instruments the lips 











206 


SOUND 


of the player act as reeds, as in the trumpet, trombone 
(Fig. 200), the French horn, and the cornet. Wind 
instruments may be classed as open or stopped pipes, 
according as the end remote from the mouthpiece is open 
or closed. 

236. Fundamental of a Closed Pipe. — Let the tall jar of 
Fig. 201 be slowly filled with water until it responds strongly to a 

c' fork, for example. The length of the column of 
air will be about 13 in. or one fourth of the wave 
length of the note. 

When the prong at a moves to b, it makes half 
a vibration, and generates half a sound wave. It 
sends a condensed pulse down the tube AB , and 
this pulse is reflected from the water at the bot¬ 
tom. Now, if AB is one fourth a wave length, the 
distance down and back is one half a wave length, 
and the pulse will return to A at the instant when 
the prong begins to move from b back to a, and to 
send a rarefaction down AB. This in turn will 
run down the tube and back, as the prong com¬ 
pletes its vibration; the co-vibration is then re¬ 
peated indefinitely, the tube responds to the fork, 
and its length is one quarter of the wave length. Hence, 

The fundamental of a closed pipe is a note whose wave 
length is four times the length of the pipe. 

237. Laws for Columns of Air. — Set vertically in a wooden 

base eight glass tubes each about 25 cm. long and 2 cm. in diameter 
(Fig. 202). Pour in them melted paraffin to close the bottom. A 
musical note may be produced by blowing a stream of air across the 
top of each tube. From the confused flutter made by the air striking 
the edge of the tube, the column of air selects for reenforcement the 
frequency corresponding to its own rate. Hence the pitch may be 
varied by pouring in water. Adjust all the tubes with water until they 
give the eight notes of the major diatonic scale. The measured lengths 
of the columns of air will be found to be nearly as 1, f, |, £, f, T 8 3 , 



A 


B 


Figure 201. — 
Fundamental of 
Closed Pipe. 














STATE OF THE AIR IN A SOUNDING PIPE 207 


The notes emitted have the 
frequencies 1, f, f, f, f, f, V, 

2 (§ 224). Hence, 

T&e frequency of a vi¬ 
brating column of air is 
inversely as its length. 

This is the principle 
employed in playing the 
trombone. 

Blow gently across the end 
of an open tube 30 

cm. long and about 2 cm. in diameter and note the pitch. 
Take another tube of the same diameter and 15 cm. long; 
stop one end by pressing it against the palm of the hand, 
and sound it by blowing across the open end. The pitch 
of the closed pipe will be the same*as that of the open one. 
The experiment may be varied by comparing the notes ob¬ 
tained by the shorter pipe when open and when closed at 
one end; the former will be an octave higher than the 
latter. Hence, 

For the same frequency, the open pipe is twice 
the length of the stopped one. 

The length of the open pipe is, therefore, half 
the wave length of the fundamental note in air. 

238. State of the Air in a Sounding Pipe.— 

Employing an open organ pipe, preferably with one glass 
side (Fig. 203), lower into it a miniature tambourine about 
3 cm. in diameter and covered with fine sand, while the 
pipe is sounding its fundamental note. The sand will be 
agitated most at the ends of the pipe and very little 
at the middle. There is, therefore, a node at the middle 
of an open pipe. A node is a place of least motion and 
greatest change of density; an antinode is a place of 
greatest motion and least change of density. The closed 



Figure 


203. — 
Node at 
Middle of 
Pipe. 



Figure 202. — Pipes for Notes of 
Major Diatonic Scale. 















































































208 


SOUND 


end of a pipe is necessarily a node, and the open end an antinode 
Hence, 

In an open pipe, for the fundamental tone, there is a 
node at the middle and an antinode at each end; in the 
stopped pipe, there is a node at the closed end and an 
antinode at the other end. 

239. Overtones in Pipes. —Blow across the open end of a glass 
tube about 75 cm. long and 2 cm. in diameter. A variety of tones 
of higher pitch than the fundamental may be obtained by varying 
the force of the stream of air. 

These tones of higher pitch than the fundamental are 
overtones; they are caused by the column of air vibrating 
in parts or segments with intervening nodes. 

Open pipes give the complete series of overtones, with fre¬ 
quencies 2, 3, 4, 5, etc. times that of the fundamental. 

In stopped pipes only those overtones are possible whose 
frequencies are 3,5, 7, etc. times that of the fundamental. 

Briefly, the reason is that with a node at one end and an 
antinode at the other, the column of air can divide into 
an odd number of equal half segments only. 

It follows that the notes given by open pipes differ in 
quality from those of closed pipes. 

XI. GRAPHIC AND OPTICAL METHODS 

240. Record of Vibrations. — Graphic methods of study¬ 
ing sound are of service in determining the frequency of 
vibration. Figure 204 shows a practical device for this 
purpose. A sheet of paper is wrapped around a metal 
cylinder, and is then smoked with lampblack. A large 
fork is securely mounted, so that a light style attached 
to one prong touches the paper lightly. The cylinder is 


MAm)METRIC FLAMES 


209 


mounted on an axis, one end of which has a screw thread 
cut in it, so that when the cylinder turns it also moves 
in the direction of its 
axis. The beats of a 
seconds pendulum may 
be marked on the paper 
by means of electric 
sparks between the style 
and the cylinder. The 
number of waves be¬ 
tween successive marks 
made by the spark is 
equal to the frequency 
of the fork. 

241. Manometric Flames. — A square box with mirror 
faces is mounted so as to turn around a vertical axis 
(Fig. 205). In front of the revolving mirrors is sup¬ 
ported a short cylinder 
A, which is divided into 
two shallow chambers 
by a partition of gold¬ 
beater’s skin or thin rub¬ 
ber. Illuminating gas 
is admitted to the com¬ 
partment on the right 
through the tube with a 
stop-cock, and burns at 
the small gas jet on the 
little tube running into 
this same compartment. 
The speaking tube is 
connected to the compartment on the other side of the 
flexible partition. 



Figure 205 . — Manometric Flame Ap¬ 
paratus. 



Figure 204 . — Inscribing the Vibrations 

















210 


SOUND 


When the mirrors are 
turned, the image of the 
gas jet is drawn out into 
a smooth band of light. 
Any pure tone at the 
mouthpiece produces alter¬ 
nate compressions and rare¬ 
factions in both chambers 
separated by the mem¬ 
brane, and these aid and 
retard the 

Figure 206 . — Manometric Flames. ^ ,. 

now ot gas 

to the burner. The flame changes shape 
and flickers, but its vibrations are too rapid 
to be seen directly. But if it is examined 
by reflection from the rotating mirrors, its 
image is a serrated band (Fig. 206). 

Koenig fitted three of these little cap¬ 
sules with jets to the side of an open organ 
pipe (Fig. 207), the membrane on the inner 
side of the gas chamber forming part of 
the wall of the pipe. When the pipe is 
blown so as to sound its fundamental tone, 
the middle point is a node with the great¬ 
est variations of pressure in the pipe, and 
the flame at that point is more violently 
agitated than at the other two, giving in 
the mirrors the top band of Fig. 206. By 
increasing the air blast, the fundamental 
is made to give way to the first overtone; 
the two outside jets then vibrate most 
strongly, and give the second band in the 
figure, with twice as many tongues of flame gas Flames. 



























THE PH ON ODEIK 


211 


as in the image for the fundamental. The third band 
may be obtained by adjusting the air pressure so that both 
the fundamental and the first overtone are produced at the 
same time. This same 
figure may be obtained 
by singing into the 
mouthpiece or funnel of 
Fig. 205 the vowel sound 
o on the note B , showing 
that this vowel sound is 
composed of a funda¬ 
mental and its octave. 

242. The Phonodeik is an instrument devised by Professor 
Dayton C. Miller to exhibit sound waves. It consists of 
a very small and thin glass mirror mounted on a minute 
steel spindle resting in jeweled 
bearings. On this spindle is a 
little pulley around which wraps 
a fine thread. One end of the 
Figure 209 . —Wave Form from thread is attached to a very thin 
Tuning Fork. glass diaphragm closing the 

small end of a resonator horn ; the other is connected to 
a delicate tension spring (Fig. 208). A small pencil of 
light is focused on the mirror by a lens and is reflected by 
the mirror to a sensitized film 
moving at right angles to it. 

Any vibration of the diaphragm 
traces on the film a wave form 

marked with all the perculiari- Figure 21 °- ^ VE FoRM 0F 
t . . Violin Tone. 

ties of the sound producing the 

vibrations of the diaphragm. These photographs are af¬ 
terwards enlarged. Fig. 209 shows the wave form caused 
by a heavy tuning fork. Fig. 210 represents the wave of 








212 


SOUND 


a violin tone, the irregulari¬ 
ties marking the overtones. 
Fig. 211 is the wave form of 
the sound of the human voice 
saying “ah.” 

Questions and Problems 

1. Name three ways in which musical sounds may differ. 

2 . Pianos are made so that the hammers strike the wires near one 
end and not in the middle. Why? 

3 . Why does the pitch of the sound made by pouring water into a 
tall cylindrical jar rise as the jar fills? 

4. What effect does a rise of temperature have on the pitch of a 
given organ pipe ? Explain. 

5 . If the pipes of an organ are correctly tuned at a temperature 
of 40° F., will they still be in tune at 90° F. ? Explain. 

6. The tones of three bells form a major triad. One of them 
gives a note a of 220 vibrations per second, and its pitch is between 
those of the other two. What are the frequencies of three bells, 
and what is the note given by the highest? 

7 . How much must the tension of a violin string be increased to 
raise its pitch a fifth (§ 223) ? 

8. If the E string of a violin is 40 cm. long, how long must a 
similar one be to give G ? 

9 . The vibration frequency of two similar wires 100 cm. long is 
297. How many beats per second will be given by the two wires 
when one of them is shortened one centimeter ? 

10. Two c' forks gave 5 beats per second when one of them was 
weighted with bits of sealing wax. Find the frequency of the weighted 
fork. 

11 . What will be the length of a stopped organ pipe to give c' of 
256 vibrations per second when the temperature of the air is 20° C.? 

12 . Calculate the length of an open organ pipe whose fundamental 
tone is one of 32 vibrations per second, and the temperature of the air 
is 20° C. 



Voice. 


QUESTIONS AND PROBLEMS 


213 


13 . An open organ pipe sounds c' (256); what notes are its two 
lowest overtones? 

14 . What is the frequency of an 8-foot stopped pipe when the 
velocity of sound is 1120 ft. per second? 

15 . Two open organ pipes 2 ft. in length are blown with air at a 
temperature of 15° and 20° C., respectively. How many beats do they 
give per second? 

16 . When the temperature of the air is such that the velocity of 
sound is 1105 ft. per second, what will be the frequency of the funda¬ 
mental note produced by blowing across one end of a tube 12.75 in. 
long, the other end being closed? What will be the frequency of its 
first overtone? 


CHAPTER VIII 


LIGHT 

I. NATURE AND TRANSMISSION OF LIGHT 

243. The Ether. — Exhaust the air as far as possible from a glass 
bell jar. Place a candle on the far side of the jar; it will be seen as 
clearly before the air has been let into the bell jar as after. 

It is obvious that the medium conveying light is not the 
air and it must be something that exists even in a vacuum. 
This medium is vaguely known as the ether. It exists 
everywhere, even penetrating between the molecules of 
ordinary matter. 

244. Light. — The prevailing view about the nature of 
light is that it is a transverse wave motion in the ether. 
Huyghens, a Dutch physicist, in 1678 proposed the theory 
that light is a wave motion; later, Fresnel, a French 
physicist, showed that the disturbance must be transverse; 
finally Maxwell modified the theory to the effect that these 
disturbances are probably not transverse physical movements 
of the ether , hut transverse alterations in its electrical and 
magnetic conditions. 

245. Transparent and Opaque Bodies. — When light falls 
on a body, in general, a part of it is reflected, a part passes 
through or is transmitted, and the rest is absorbed. A 
body is transparent when it allows light to pass through it 
with so little loss that objects can be easily distinguished 
through it, as in the case of clear glass, air, pure water. 
Translucent bodies transmit light, but so imperfectly that 

214 



Niagara Falls Power Plant. 

Used for light and power in several cities of New York State. 














SPEED OF LIGHT 


215 


objects cannot be seen distinctly through them, as horn, 
oiled paper, very thin sheets of metal or wood. Other 
bodies, such as blocks of wood or iron, transmit no light, 
and these are opaque. No sharp line of separation between 
these classes can be drawn. The degree of transparency 
or opacity depends on the nature of the body, its thick¬ 
ness, and the wave length (§ 310) of the light. Water 
when deep enough cuts off all light; the bottom of the 
deep ocean is dark. Stars invisible at the foot of a moun¬ 
tain are often visible at the top; bodies opaque to light of 
one wave length are often transparent to light of a differ¬ 
ent wave length. 

246. Speed of Light. — Previous to the year 1676 it was 
believed that light traveled infinitely fast, because no one 
had found a way 
to measure so 
great a velocity. 

But in that year 
Roemer, a young 
Danish astron¬ 
omer, made the 
very important 
discovery that 
light travels with 
finite speed . 

Roemer was en¬ 
gaged at the 
Paris Observa¬ 
tory in observing the eclipses of the inner moon of the 
planet Jupiter. At each revolution of the moon M (Fig* 
212) in its orbit around the planet J", it passes into the 
shadow of the planet and becomes invisible from the earth 
at E, or is eclipsed. By comparing his observations with 



Figure 212 . — Speed of Light from Jupiter’s 
Inner Moon. 






216 


LIGHT 


much earlier recorded ones, Roemer found that the mean in¬ 
terval of time between two successive eelipses was 42.5 
hours. From this it was easy to calculate in advance the 
time at which succeeding eclipses would occur. But when 
the earth was going directly away from Jupiter, as at E v the 
eclipse interval was found to be longer than anywhere else; 
and at U 2 , across the earth’s orbit from Jupiter, each eclipse 
occurred about 1000 sec. later than the predicted time. 
To account for this difference Roemer advanced the theory 
that this interval of 1000 sec. is the time taken by light 
to pass across the diameter of the earth’s orbit. This gave 
for the speed of light 309 million meters, or 192,000 miles 
per second. 

Later determinations in our own country by Michelson 
and Newcomb show that the speed of light is 299,877 km., 
or 186,337 mi. per second. 

247. Direction of Propagation. — Place a sheet-iron cylinder 
over a strong light, such as a Welsbach gas lamp, in a darkened room. 
The cylinder should have a small hole opposite the light. Stretch a 
heavy white thread in the light streaming through the aperture. 
When the thread is taut it is visible throughout its entire length, but 
if permitted to sag it becomes invisible. 

The experiment shows that light travels in straight lines. 
It will appear later that this is true only when the medium 
through which light passes has the same physical proper¬ 
ties in all directions. 

248. Ray, Beam, Pencil. — Light is propagated outward 
from the luminous source in concentric spherical waves, 
as sound waves in air from a sonorous body. Rays are 
the radii of these spherical waves , and they are, therefore, 
normal (perpendicular) to them. They mark the direc¬ 
tion of propagation. 

When the source of light is at a great distance, the rays 


SHADOWS 


217 


incident on any surface are sensibly parallel. A number 
of parallel rays form a beam of light. For example, in the 
case of light from the sun or stars, the distance is so great 
that the rays are sensibly parallel. Rays of light pro¬ 
ceeding outward from a point form a diverging pencil; 
rays proceeding toward a point, a converging pencil. 

249. Shadows. — Place a ball between a lighted lamp and a white 
screen. From a part of this screen the light will be wholly cut off, 
and surrounding this area is one from which the light is excluded in 
part. If three small holes be made in the screen, one where it is 
darkest, one in the part where it is less dark, and one in the lightest 
part, it will be found when one looks through them that the flame of 
the lamp is wholly invisible through the first, a part of it is visible 
through the second, and the whole flame through the third. 

The space behind the opaque object from which the 
light is excluded is called the shadow. The figure on 
the screen is a section of the shadow. The darkest part 
of the shadow, called the umbra , is caused by the total 
exclusion of the light by the opaque object; the lighter 
part, caused by its partial exclusion, is called the penumbra. 



When the source of light is a point L (Fig. 213), the 
shadow will be bounded by a cone of rays, ALB, tangent 
to the object, and will have only one part, the umbra. 
When the source of light is an area, such as LL (Fig. 214), 
the space ABBC behind the opaque body receives no light, 
and the parts between AC 7 and A O', and between BD and 








218 


LIGHT 


BD\ receive some light, the amount increasing as A O' 
and BD r are approached. From these figures the cases 
when the luminous body is larger than the opaque body, 



Figure 214. — Source of Light an Area. 


and when it is of the same size, may be understood and 
illustrated by the student. 

250. Images by Small Openings. — Support two sheets of card¬ 
board (Fig. 215) in vertical and parallel planes. In the center of one 

cut a hole H about 2mm. 
square and in front of it place 
a lighted candle or lamp. An 
inverted image of the flame 
will appear on the other sheet 
if the room is dark. The area 
of the image will vary with any 
change in the position of the 
screen or candle, the bright¬ 
ness with the size of the aperture, but no change in the shape of the 
aperture affects the image. With a larger aperture the image gains 
in brightness but loses in definition. 

Every point of the candle flame is the vertex of a cone 
of rays, or a diverging pencil, passing through the opening 
and forming an image of it on the screen. These numer¬ 
ous pictures of the opening overlap and form a picture of 
the flame, and the number at any one place determines 
the brightness. The edge of the image will therefore be 
less bright than other portions. In the case of a large 


i - 


Figure 215. — Image by Small Opening. 

















LAW OF INTENSITY 


219 


opening, the overlapping of the images of the aperture 
destroys all resemblance between the image and the object, 
the resulting image having the shape of the aperture. 

251. Illustrations. — The pinhole camera is an applica¬ 
tion of the foregoing principle. It consists of a small 
box, blackened within, and provided with a small opening 
in one face (Fig. 216) ; the light passes through this and 
forms an image on the sensitized plate placed on the oppo- 



Figure 216 . — Pinhole Camera. 


site side. When the sun shines through the small chinks 
in the foliage of a tree, a number of round or oval spots 
of light may be seen on the ground. These are images of 
the sun. During a partial solar eclipse such figures as¬ 
sume a crescent shape. 

II. PHOTOMETRY 

252. Law of Intensity. — The intensity of illumination is 
the quantity of light received on a unit of surface. Every¬ 
day experience shows that it varies, not only with the 
source of the light, but also with the distance at which 
the source is placed. 

Cut three cardboard squares, 4, 8, aDd 12 cm. on a side respectively, 
and mount them on supports (Fig. 217). The centers of these screens 
should be at the same distance above the table as the source of light. 













220 


LIGHT 


Use a Welsbach gas lamp with an opaque chimney having a small 
opening opposite the center of the light, and set it 99 cm. from the 
largest screen. Place the medium-sized screen so that it exactly cuts 
off the light from the edges of the largest. In like manner place the 
smallest screen with respect to the intermediate one. If these screens 
are placed with care, it will be found that their distances from the 
light are 33, 66, and 99 cm. respectively, or as 1: 2: 3. Now as each 
screen exactly cuts off the light from the one next farther away, it 



follows that each receives the same amount of light from the source 
when the light is not intercepted. The surfaces of the screens are as 
1:4:9, and hence the quantity of light per unit of surface must be 
inversely as 1: 4: 9, the square of 1, 2, and 3 respectively. 

This experiment shows that the intensity of illumination 
varies inversely as the square of the distance from the source 
of light. If the medium is such as to absorb some of the 
light, the decrease in intensity is greater than that ex¬ 
pressed by the law of inverse squares. 

This law of illumination assumes that the source of 
light is a point, and that the receiving surface is at right 
angles to the direction of the rays. When the surface on 
which the light (and heat) falls is inclined, the intensity 
is still less. In northern latitudes the earth is nearer the 
sun in winter than in summer, but the intensity of the 
radiation received is less than in summer, because the alti- 

















THE BUNSEN PHOTOMETER 


221 


tude of the sun at noon is less, that is, because the earth’s 
surface is more inclined to the direction of the radiations. 

253. The Bunsen Photometer. —A photometer is an instru¬ 
ment for comparing the intensity of one light with that of 
another. The principle applied is a consequence of the 
law of the intensity of illumination; it is that the ratio 
of the intensities of two lights is equal to the square 
of the ratio of the distances at which they give equal 
illumination. 

In the Bunsen photometer a screen of paper A (Fig. 
218), having a translucent spot made by applying a little 



Figure 218 . — Bunsen Photometer. 

hot paraffin, is supported on a graduated bar between a 
standard candle B and the light 0 to be compared with 
it. An old but imperfect standard candle is the light 
emitted by the sperm candle of the size known as “ sixes,” 
when burning 120 grains per hour. The photometer 
screen is usually inclosed in a box open toward the two 
lights, and back of it are two mirrors placed with their 
reflecting sides toward each other in the form of a V, so 
that the observer standing by the side of A can see both 
sides of the screen by reflection in the mirrors. The 






222 


LIGHT 


position of A or of B may then be adjusted until both 
sides of the screen look alike. Then the intensity of 0 
is to the intensity of B as A O 2 is to AB f 2 . 

In the Joly photometer two rectangular blocks of 
paraffin, separated by a sheet of tinfoil, take the place of 
the sheet of paper. When the lights are balanced the 
edges of the paraffin blocks are equally lighted. 

Questions and Problems 

1. What is the cause of an eclipse of the sun ? Explain by diagram 

2. What is the cause of an eclipse of the moon ? Explain by dia- 
gram. 

3 . Why does a small aperture in the camera give a more sharply 
defined image than a large oi;e? 

4 . Why is a larger aperture in the camera necessary for a snapshot 
than for a time exposure ? 

5 . In an attempt to determine the height of a tree the following 
data were obtained: Length of the tree’s shadow, 50 ft.; length of the 
shadow of a vertical 10-ft. pole, 4 ft. What is the height of the tree \ 

6. Two lights, 25 and 100 c.p. respectively, are placed 60 ft. apart. 
Where must a screen be placed between them and on the line joining 
them so as to be equally illuminated on its two sides? 

7 . In measuring the candle power of a lamp the following data were 
obtained: Distance of the standard lamp from the photometer disk, 
20 cm.; distance of lamp, 120 cm. What is the candle power? 

8 . If a book can be read at a distance of 1 ft. from a 20 c.p. electric 
lamp, at what distance from a 60 c.p. lamp can it be read with equal 
clearness? 

9 . The picture of a tree taken with a pinhole camera was 10 cm. 
long. The aperture was 20 cm. from the sensitive plate and 30 m. 
from the tree. What is the height of the tree ? 

10. Two Mazda lamps are to be used to give equal illumination to 
the two sides of a screen. One of them is 20 c.p. and distant 8 ft. 
from the screen; the other is 40 c.p. How far from the screen must 
the second lamp be placed to secure the desired illumination ? 


LAW OF REFLECTION 


223 


11 . What is the length of the umbra of the earth’s shadow, the 
diameter of the earth and sun being 8000 and 880,000 miles respec¬ 
tively, and the distance from the center of the earth to that of the 
sun being 93,000,000 miles ? 

III. REFLECTION OF LIGHT 

254. Regular Reflection.—When a beam of light falls 
on a polished plane surface, the greater part of it is re¬ 
flected in a definite di¬ 
rection. This reflec¬ 
tion is known as regu¬ 
lar reflection. In Fig. 

219 a beam of light IB 
is incident on the plane 
mirror B and is re¬ 
flected as BR. IB is 
the incident beam , BR 
is the reflected beam , the 
angle IBP between the incident beam and the normal 
(perpendicular) to the reflecting surface is the angle of 
incidence , and the angle PBR between the reflected beam 
and the normal is the angle of reflection. 

255. Law of Reflection. — On a semicircular board are mounted 
two arms, pivoted at the center of the arc (Fig. 220). One arm 
carries a vertical rod P, and the other a paper tube T with parallel 

threads stretched 
across a diameter at 
each end. A plane 
mirror M is mounted 
at the center of the 
semicircle, with its 
reflecting surface 
parallel to the di¬ 
ameter at the ends 

Figure 220. — Law of Reflection. of the arc. On the 




Figure 219. — Incidence and Reflection. 

































224 


LIGHT 


edge of the semicircle is a scale of equal parts with the zero on the 
normal to the mirror. Place the arm P in any desired position and 
move the arm T until the image of the rod in the mirror is exactly in 
line with the two threads. The scale readings will show that the two 
arms make equal angles with the normal to the mirror. Hence, 

The angle of reflection is equal to the angle of inci¬ 
dence; and the incident ray, the normal, and the reflected 
ray all lie in the same plane . 

256. Diffused Reflection. — Cover a large glass jar with a piece 
of cardboard, in which is a hole about 1 cm. in diameter. Fill the 
jar with smoke, and reflect into it through the hole in the cover a 
beam of sunlight. The whole of the interior of the jar will be 
illuminated. 

The small particles of smoke floating in the jar furnish 
a great many reflecting surfaces; the light falling on 
them is reflected in as many directions. The scattering of 
light by uneven or irregular surfaces is diffused reflection . 

To a greater or less extent all reflecting surfaces scat¬ 
ter light in the same way as the smoke particles. Figure 

221 illustrates in an 
exaggerated way the 
difference between 
a perfectly smooth 
surface and one 
Figure 221 . — Regular and Diffused Reflec- somewhat uneven. 

■ TI0N ‘ It is by diffused re¬ 

flection that objects become visible to us. Perfect reflec¬ 
tors would be invisible; it is almost impossible to see the 
glass of a very perfectly polished mirror. The trees, the 
ground, the grass, and particles floating in the air reflect 
the light from the sun in every direction, and thus fill the 
space about us with light. If the air were free from all 
floating particles and gases, the sky would be dark in all 





IMAGE IN A PLANE MIRROR 


225 


directions, except in the direction of the sun and the stars. 
This conclusion is confirmed by aeronauts who have reached 
very high altitudes, where there was almost a complete ab¬ 
sence of floating particles. 

257. Image in a Plane Mirror. —Any smooth reflecting 
surface is called a mirror. A plane mirror is one whose 
reflecting surface is a plane. A spherical mirror is one 
whose reflecting surface is a portion of a sphere. 

Support a pane of clear window glass in a vertical position, and 
place a red-colored lighted candle back of it. Place a white un¬ 
lighted candle in front. Move the unlighted candle until its image 
in the glass as a mirror coincides exactly with the lighted candle seen 
through the glass. The distance of the two candles from the mirror 
will be the same. 

Let A be a luminous point in front of a plane mirror 
MN (Fig. 222). The group of waves included between 
the rays AB and AO after a d 

reflection proceed as if from 
A', situated on the normal 
AK and as far behind the 
reflecting surface as A is in 
front of it. An eye placed 
at DB receives these waves 
as if they came directly from 
a source A'. The point A! 
is called the image of A in 
the mirror MN. It is known 
as a virtual image, because 
the light only appears to 
come from it. Therefore, Figure 222. — Position of Image of 
the image of a point in a A PoiNT - 

plane mirror is virtual, and is as far back of the mirror as the 
point is in front . The image may be found by drawing 




226 


LIGHT 


from the point a perpendicular to the mirror, and pro¬ 
ducing the perpendicular until its length is doubled. 

258. Construction for an Image in a Plane Mirror. —As 
the image of an object is composed of the images of its 
points, the image may be located by finding those of its 

points. Let AB (Fig. 223) 
represent an object in front of 
the plane mirror MN. Draw 
perpendiculars from A and B 
to the mirror and produce them 
until their length is doubled. 
f A'B r is the image of AB. It 
is virtual, erect, and of the 
Figure 223. — Construction of game s i ze as the object. 

Image. j 

An image in a plane mirror 

is reversed from right to left. This is clearly seen when 
a printed page is held in front of a mirror, the letters all 
being reversed, or perverted , as it is termed. Otherwise 
the image is so like the object that illusions are produced, 
because a well-polished mirror itself is invisible. 

In general, the image in a plane mirror is the same size 
as the object , is virtual, and is as far back of the mirror as 
the object is in front. 

259. Path of the Rays to the Eye. — It is important to 
notice that the image of any fixed object is fixed in space, 
and is entirely independent of the position of the observer. 
The paths of the rays for the image for one observer are 
not the same as those for another. 

Let AB (Fig. 224) represent an object in front of the 
plane mirror MN. Drop perpendiculars from points of 
the object to the mirror, and produce them until their 
length is doubled. In this manner the image of AB is 
found at A!B' . Let E and E’ be the position of the eye 





USES OF A PLANE MIRROR 


227 


for two observers. To find the path of the rays entering 
the eye at E, draw lines from A! and B’ to E. These 
lines are the directions in which the light enters the eye 
from A! and B’ respectively. 

But no light comes from be¬ 
hind the mirror, and so the in¬ 
tersections of these lines with 
the mirror are the points where 
the rays from A and B are re¬ 
flected to E. In a similar man¬ 
ner the path of the rays may 
be traced for the position of 
the eye at E r . The full lines 
in front of the mirror are the 
paths of the rays from A and 
B, which give the images at 
A! and B’. . 

260. Uses of a Plane Mirror. — The employment of the 
plane mirror as a “ looking glass ” dates from a period of 
great antiquity. The process of covering a glass surface 
with an amalgam of tin and mercury came into use in 
Venice about three centuries ago. The process of cover¬ 
ing glass with a film of silver was invented during the 
last century. 

The fact that the image in a plane mirror is virtual has 
been used to produce many optical illusions, such as the 
stage ghost, the magic cabinet, the decapitated head, etc. 
To produce the illusion of a ghost, a large sheet of un¬ 
silvered plate glass, with its edges hidden by curtains, 
is so placed that the audience has to look obliquely 
through it to see the actors on the stage. Other actors, 
hidden from direct view, and strongly illuminated, are seen 
by reflection in the glass as ghostly images on the stage. 



the Eye. 





228 


LIGHT 


261. Multiple Reflection. — Place two mirrors so that their re¬ 
flecting surfaces form an angle (Fig. 225). If a lighted candle be 

placed between them, several images 
may be seen in the mirrors; three 
when they are at right angles, more 
when the angle is less than a right 
angle. When the mirrors are parallel, 
all the images are in a straight line 

. perpendicular to the mirrors. 

Figure 225.— Multiple r r 

Reflection. The image in one mirror 

serves as an object for the second mirror, and the image in 
the second becomes in turn an object for the first mirror. 
In Fig. 226 the two mirrors are at right angles. O' is the 
image of 0 in AB , and is found as in § 258. O'" is the 

image of O' in AC, and is found by the line O' 0" f drawn 
perpendicular to AC produced. 0" is the image of 0 in 
A (7, and since the mirrors are 
at right angles, O'" is also 
the image of 0" in AB. O'" 
is situated behind the plane 
of both mirrors, and no im¬ 
ages of it can be formed. 

All the images are situated 
in the circumference of a 
circle whose center is A and 
radius AO. If ^£7 is the po¬ 
sition of the eye, then O' 
and 0" are each seen by one 
reflection, and O'" by two reflections, and for this reason 
it is less bright. To trace the path of a ray for the image 
O '", draw O'" E, cutting AB at b , and from the intersec¬ 
tion b draw bO", cutting AC at a. Join aO ; the path of 
the ray is OabE. It is interesting to find the images when 
the mirrors are at various angles. 



Figure 226. — Mirrors at Right 
Angles. 










SPHERICAL MIRRORS 


229 


262. Illustrations. — The double image of a bright star and the 
several images of a gas jet in a thick mirror (Fig. 227) are examples 
of multiple reflection, the front surface of the mirror and the metallic 
surface at the back serving as parallel reflectors. Geometrically the 
number of images is infinite; 

but on account of their faint¬ 
ness only a limited number is 
visible. The kaleidoscope , a toy 
invented by Sir David Brewster, 
is an interesting application of 
the same principle. It consists 
of a tube containing three mir¬ 
rors extending its entire length, 
the angle between any two of 
them being 60°. One end of the 
tube is closed by ground glass, 
and the other by a cap with n 
round hole in it. Pieces of 
colored glass are placed loosely 
between the ground glass and a 
plate of clear glass parallel to 
it. On looking through the 
hole at any source of light, 
multiple images of these pieces 

of glass are seen, symmetrically arranged around the center, and form¬ 
ing beautiful figures, which vary in pattern with every change in the 
position of the pieces of glass. 

263. Spherical Mirrors. — A mirror is spherical when its 
reflecting surface is a portion of the surface of a sphere. 
If the inner surface is polished for reflection, the mirror 

is concave ; if the outer surface, it is 
convex. Only a small portion of a 
spherical surface is used as a mirror. 
In Fig. 228 the center C of the mirror 
MN is the center of curvature of the 
sphere of which the reflecting surface 
is a part. The middle point A of the 



Figure 227. — Multiple Images. 



Figure 228. — Spherical 
Mirror. 














230 


LIGHT 


reflecting surface MN is the pole or vertex of the mirror, 
and the straight line AB passing through the center of 
curvature 0 and the pole A of the mirror is its principal 
axis. Any other straight line through the center and in¬ 
tersecting the mirror is a secondary axis. The figures of 
spherical mirrors in this chapter are sections of a sphere 
made by passing a plane through the principal axis. 

The difference between a plane mirror and a spherical 
one is that the normals to a plane mirror are all parallel 
lines, while those of a spherical mirror are the radii of the 
surface, and all pass through the center of curvature. 

264. Principal Focus of Spherical Mirrors. — A focus is 
the point common to the paths of all the rays after inci¬ 
dence. It is a real focus if the rays of light actually pass 
through the point, and virtual if they only appear to 
do so. 


Let the rays of the sun fall on a concave spherical mirror. Hold a 
graduated ruler in the position of its principal axis, and slide along 
it a small strip of cardboard. Find the 
point where the image of the sun is small¬ 
est. This will mark the principal focus, 
and it is a real one. If a convex spherical 
mirror be used the light will be reflected 
as a broad pencil diverging from a point 
back of the mirror: The focus is then a 
virtual one. 

Figure 229. — Principal 

Focus, Concave Mirror. A a pencil of rays parallel to the 
principal axis falls on a concave 
spherical mirror, the point to which the rays converge after 
reflection is called the principal focus of the mirror (Fig. 
229). In the case of a convex spherical mirror, the prin¬ 
cipal focus is the point on the axis behind the mirror from 
which the reflected rays diverge (Fig. 230). The dis- 













POSITION OF THE PRINCIPAL FOCUS 


231 



Figure 230. — Principal Fo¬ 
cus, Convex Mirror. 


L 

/ r E 

1 

2k 

4 

i *V 

B 


tance of the principal focus from 
the mirror is its principal focal 
length. 

265. Position of the Principal 
Focus. — Let MN (Fig. 231) be 
a concave mirror whose center is 
at C ajid principal axis is AB. 

Let ED be a ray parallel to BA .. 

Then CD is the normal at D; 
and CDF , the angle of reflection, must equal EDC\ the 
angle of incidence. Since the ray BA is normal to the 
mirror, it will be reflected back 
along AB. The reflected rays DF 
and AB have a common point F , 
which is the principal focus. The 
triangle CFD is isosceles with the 
sides CF and FD equal. (Why ?) 
But when the point D is near A, 
FD is equal to FA ; F is therefore 
the middle point of the radius CA. 
Other rays parallel to BA will pass after reflection nearly 
through F. Hence, the principal focus of a concave spheri¬ 
cal mirror is real and is halfway between the center of curva¬ 
ture and the vertex. 

Let MN (Fig. 232) be a 
convex spherical mirror. ED 
and BA are rays parallel to 
the principal axis. When 
produced back of the mirror, 
after reflection, their common 
point F is back of the mirror 
and halfway between A and O. Fioure 232 _ Pr ' )cipal Focus VlR . 
(Why ?) Hence, the princi- tual for Convex Mirror. 


Figure 231. — Position of 
Principal Focus. 

















232 


LIGHT 


pal focus of a convex spherical mirror is virtual and halfway 
between the center of curvature and the mirror. 

266. Conjugate Foci of Mirrors. — When a diverging pen¬ 
cil of light ABB (Fig. 233) falls on the spherical mirror 

MN, it is focused after 
reflection at a point B' 
on the axis AB which 
passes through the ra¬ 
diant point or source 
of light ; after reflec¬ 
tion the rays diverge 



Figure 233. — Conjugate Foci, Concave 
Mirror. 


new radiant point. When rays diverging from one point 
converge to another, the two points are called conjugate 
foci. 

In Fig. 234, the rays BA and BB diverge from B as the 
radiant point; after reflection they diverge as if they 
came from B' behind the 

M 
D 


reflecting surface ; B' is Tr 
a virtual focus and B 
and B' are conjugate 
foci. 

In the first case the 
source of light is farther 
from the mirror than the 



Figure 234. — Conjugate Foci, One 
Focus Virtual. 


center of curvature, and the focus is real ; in the second 
case it is nearer the mirror than the principal focus, and 
the focus is virtual. 1 


1 In Fig. 233, CD bisects the angle BDH. Hence, — = —. If D 
b & ’ B'D B'C 

is close to A, we may, without sensible error, place BD = BA and 
B'D = B'A. Put BA = p, B'A — q , CA = r = 2/. Then BC = p —V, 
p p — r 1121 

B'C = r-q, and - = from which p + - = -=j. By measuring p 







IMAGES IN SPHERICAL MIRRORS 


233 


267. Images in Spherical Mirrors. — In a darkened room sup¬ 
port on the table a concave spherical mirror, a candle, and a small 
white screen. Place the candle anywhere beyond the focus, and move 
the screen until a clear image of 
the flame is formed on it (Fig. 

235). Notice the size and position 
of the image, and whether it is 
erect or inverted. When the can¬ 
dle is between the focus and the 
mirror, an image of it cannot be 
obtained on the screen, but it can 
be seen by looking into the mirror. Figure 235. Image by Concave 
The same is true for the convex Mirror. 

mirror, whatever be the position of the candle; in these last cases the 
image is a virtual one. 



The experiment shows the relative positions of the 
object and its image for a concave mirror, all depending 

on the position of 
the object with re¬ 
spect to the mirror. 
If these positions 
are carefully noted 
it will be seen that 

there are six dis- 

Figure 236. — Object Beyond Center of Curva- tinct cageg ag fol _ 

TURE. _ 

lows : 

First. — When the object ( AB , Fig. 236) is at a finite 
distance beyond the center of curvature, the image is real, 
inverted, smaller than the object, and between the center 
of curvature and the principal focus. 

Second. — When a small object is at the center of curva¬ 
ture, the image is real, inverted, of the same size as the 



and q, we may compute r and /. For the convex mirror, q and r are 
negative. 











234 


LIGHT 


object, and at the center of curvature 
(Fig. 237). 

Third. — When the object is between 
the center and the principal focus, the 
image is real, inverted, larger than the 
object, and is beyond the center (Fig. 
238). This is the converse of Case I. 

Fourth. — When the object is at the 
principal focus, the rays are reflected 
parallel and no distinct image is formed (Fig. 239). 

Fifth. — When the ob¬ 
ject is between the prin¬ 
cipal focus and the mir¬ 
ror, the image is virtual, 
erect, and larger than 
the object (Fig. 240). 

Sixth. — When the 
mirror is convex, the 
image is always virtual, 
erect, and smaller than 
the object (Fig. 241). 

268. Construction for 
Images. — To find images 
in spherical mirrors by geometrical construction, it is only 

necessary to find conjugate 
focal points. To do this 
trace two rays for each point 
for the object, one along the 
secondary axis through it, 
and the other parallel to the 
principal axis. The first ray 
is reflected back on itself, 
and the second through the 



Figure 239. — Object at Princi¬ 
pal Focus. 



Figure 238. — Object Between Center 
and Principal Focus. 



Figure 237.— Ob¬ 
ject at Center of 
Curvature. 














SPHERICAL ABERRATION IN MIRRORS 


235 





Figure 240. — Object between 
Principal Focus and Mirror. 


principal focus. The intersection of the two reflected rays 
from the same point of the object locates the image of that 
point. 

For instance: In Fig. 236, 

AC is the path of both the 
incident and the reflected ray, 
while the ray AD is reflected 
through the principal focus 
F. Their intersection is at 
a. The rays BO and BE are 
reflected similarly through b. 

Hence, ah is the image of 
AB. In Fig. 240, the ray 
AC along the secondary axis, and AD reflected back 
through F as DF, must be produced to meet back of the 
mirror at the virtual focus a. A and a are conjugate foci; 

also B and 6, and ab is 
a virtual image. 

For the convex mir¬ 
ror (Fig. 241) the con¬ 
struction is the same. 
From the point A draw 
A C along the normal or 
secondary axis, and AD 
parallel to the principal 
axis. The latter is re¬ 
flected so that its direc¬ 
tion passes through F. 
The intersection of these two lines is at a. The image 
ab is virtual and erect. 



Figure 241. — Image Always Virtual in 
Convex Mirror. 


269. Spherical Aberration in Mirrors. — Bend a strip of bright 
tin into as true a semicircle as possible and fasten it to a vertical 
board as in Fig. 242. At right angles to the board at one end place 










236 


LIGHT 


a vertical sheet of cardboard containing three parallel slots. Send a 
strong beam of light through each of these slots; the three beams will 
be reflected by the curved tin through different points, the beam 

nearest the straight rim 
of the mirror crossing 
the axis nearest the mir¬ 
ror. 


The experiment 
shows that rays in¬ 
cident near the mar¬ 
gin of a spherical 
mirror cross the axis 
after reflection be¬ 
tween the principal focus and the mirror. This spreading 
out of the focus is known as spherical aberration by reflec¬ 
tion. It causes a lack of sharpness in the outline of 
images formed by spherical mirrors. It is reduced by 
decreasing the aperture of the mirror by means of a dia¬ 
phragm to cut off marginal rays, 
or by decreasing the curvature of 
the mirror from the vertex out¬ 
ward. The result then is a para¬ 
bolic mirror (Fig. 243), which 
finds use in searchlights, light¬ 
houses, headlights of locomotives 
and automobiles, and in reflecting 
telescopes. 

270. Caustics by Reflection. — Use Figure 243 - Parabolic 

IRROR 

the tin reflector of the last experi¬ 
ment as shown in Fig. 244. The light from a candle or a 
lamp is focused on a curved line. 

The curve formed by the rays reflected from a spherical 
mirror is called the caustic by reflection. It may be seen 





























The 100-Inch Silvered Parabolic Mirror of the Mt. Wilson Solar Observatory. 
It is 14 inches thick and weighs 4| tons. Its focal length is about 50 feet. 




































































' 

























































































. 










































. 











QUESTIONS AND PROBLEMS 


237 


by letting sunlight fall on a tin milk pail partly full of 
milk, or on a plain gold ring on a white surface. 



Figure 244 . — Caustic by Reflection. 


Questions and Problems 

1. Why is the image of an object seen in the bowl of a silver spoon 
distorted ? 

2. Show by an arrangement of plane mirrors how to see around an 
obstruction. 

3 . How can a concave, a convex, and a plane mirror be distinguished 
from one another, even when their outer surfaces are flat, as is often 
the case ? 

4 . Construct all the images that would be formed of a luminous 
point placed between two mirrors forming an angle of 60°. 

5 . Show by a diagram that a person can see his whole length in a 
short plane mirror placed on a vertical wall by tipping the top of the 
mirror forward and standing close to the mirror. 

6. A candle foot is the intensity of illumination of a 1 c.p. 
light at a distance of one foot from the illuminated surface. What 
will be the illumination in foot candles of a surface 10 ft. away from 
a 50 c.p. lamp ? 











238 


LIGHT 


7 . How far must a surface be from a 40 c.p. lamp to receive the 
same illumination as it would receive from a 4 c.p. lamp two feet 
distant ? 

8. If a person can just see to read a book when 10 ft. away from a 
16 c.p. lamp, how far away from a 1600 c.p. arc light can he see to 
read the book? 

9. Where must a 16 c.p. lamp be placed between two parallel walls 
of a room 20 ft. apart in order that one wall may be four times as 
strongly illuminated as the other? 

10 . A gas burner consuming 5 cu. ft. per hour gives a flame of 16 
c.p. A 16 c.p. electric bulb consumes 44 watts per hour. With gas 
at $1 per 1000 cu. ft. and electricity at 12£ cents per K. W. hour, 
which is the cheaper? 

11. If an object is 18 ft. distant from a concave spherical mirror 
and the image formed of it is 2 ft. from the mirror, what is its focal 
length ? 

12. Find by a diagram what effect it has on the image of an object 
in a convex spherical mirror to vary the distance of the object from 
the mirror. 

13 . The mirror formula applies equally well to the convex spheri¬ 
cal mirror if q , r, and / are made negative. Find the position of the 
image of an object as given by a convex spherical mirror when the 

radius of curvature is 20 inches, 
the object being 10 ft. from the 
mirror. 

14 . If a plane mirror is moved 
parallel to itself directly away 
from an object in front of it, 
show that the image moves twice 
as fast as the mirror. 

IV. REFRACTION OF LIGHT 

271. Refraction. — Fasten a 

Figure 245. — Refraction of Light. P a P er protractor scale centrally 

on one face of a rectangular bat¬ 
tery jar (Fig. 245), and fill the jar with water to the horizontal di¬ 
ameter of the scale. Place a slotted cardboard over the top. With 
















CAUSE OF REFRACTION 


239 


a plane mirror reflect a beam of light through the slit into the jar, at 
such an angle that the beam is incident on the water exactly back of 
the center of the seale. The path of this ribbon of light may be 
traced; its direction is changed at the surface of the water. 

The change in the course of light in passing from 
one transparent medium into another is called refraction. 

Place a coin at the bottom of an 
empty cup standing on a table, and 
let an observer move back until the 
coin just passes out of sight below the 
edge of the cup; now pour water into 
the cup, and the coin will come into 
view (Fig. 246). 

The changes in the apparent depth 
of a pond or a stream, as the observer 
moves away from it, are caused by re¬ 
fraction. The broken appearance of a 
straight pole thrust obliquely into 
water is accounted for by the change 
in direction which the rays coming from the part under water suffer 
as they emerge into the air. 

272. Cause of Refraction. — Foucault in France and 

Michelson in America 
have measured the veloc¬ 
ity of light in water, and 
have found that it is only 
three-fourths as great as 
in air. The velocity of 
light in all transparent 
liquids and solids is less 
than in air, while the 
velocity in air is practi¬ 
cally the same as in a 
vacuum. 

If now a beam of light 



Figure 247. — Refraction Explained. 



Figure 246. — Cup of Water 
and Coin. 


























240 


LIGHT 


is incident obliquely on the surface MN of water (Fig. 
247), all parts of a light wave do not enter the water at the 
same time. Let the parallel lines perpendicular to AB 
represent short portions of plane waves. Then one part 
of a wave, as/, will reach the water before the other part, 
as e, and will travel less rapidly in the water than in the 
air. The result is that each wave is swung around, that 
is, the direction of propagation BO , which is perpendicular 
to the wave fronts, is changed; in other words, the beam 
is refracted. The refraction of light is, therefore, due 
to its change in velocity in passing from one transparent 
medium to another. 

273. The Index of Refraction. — Let a beam of light pass 
obliquely from air to water or glass, and let AB (Fig. 248) 
be the incident wave front. From 
A as a center and with a radius 
AT) equal to the distance the light 
travels in the second medium 
while it is going from B to 0 in 
air, draw the dotted arc. This 
limits the distance to which the 
disturbance spreads in the second 
medium. Then from 0 draw CD 
tangent to this arc and draw AD to the point of tangency. 
CD is the new wave front. 

The distances B C and AD are traversed by the light in 
the same time. They are therefore proportional to the 
velocities of light in the two media. Then the 

Index of r fraction = : JP"* <lf *» «* = v / 

speed in second medium v' 


N 



1 The older mathematical definition of the index of refraction is the 
ratio of the sine of the angle Qf incidence to the sine of the angle of re- 







LAWS OF REFRACTION 


241 


The angle NOB is the angle of incidence. It is equal 
to the angle BAO between the incident wave front and 
the surface of separation of the two media. The angle of 
refraction is the angle N'AD. It is equal to the angle 
ACD between the wave front in the second medium and 
the surface of separation. The angle at (7, between the 
direction of the incident ray and the refracted ray, is the 
angle of deviation. 

The following are the indices of refraction for a few 
substances: 

Water . . „ .1.33 Crown glass . . 1.51 

Alcohol . . . .1.36 Flint glass 1.54 to 1.71 

Carbon bisulphide 1.64 Diamond .... 2.47 

For most purposes the index of refraction for water may 
be taken as |, for crown glass f, for flint glass ^ and for 
diamond \. 

274. Laws of Refraction. — The following laws, which 
summarize the facts relative to single refraction, were 
discovered by Snell, a Dutch physicist, in 1621: 

I. When a pencil of light passes obliquely from a less 
highly to a more highly refractive medium, it is bent 
toward the normal; when it passes in the reverse direc¬ 
tion, it is bent from the normal. 

II. Whatever the angle of incidence, the index of re¬ 
fraction is a constant for the same tivo media. 

fraction. Now the sine of an angle in a right triangle is the quotient of 
the side opposite by the hypotenuse. Thus, the sine pf angle BAC is 

—, and the sine of ACD is Dividing one by the other, the common 

AC AC v 

term AC cancels out, and the index of refraction equals ^, as before. 

The two definitions are therefore equivalent to each other. For the con¬ 
struction to find the refracted ray, see the Appendix. 



242 


LIGHT 


III. The planes of the angles of incidence and refrac¬ 
tion coincide. 

275. Refraction through Plate Glass. —Draw a heavy black 
line on a sheet of paper, and place over it a thick plate of glass, cover¬ 
ing a part of the line. Look obliquely through 
the glass; the line will appear broken at the edge 
of the plate, the part under the glass appearing 
laterally displaced (Fig. 249). 


Figure 249. — 
Image of Line Dis¬ 
placed. 


To explain this, let MN (Fig. 250) 
represent a thick plate of glass, and AB 
a ray of light incident obliquely upon it. 
If the path of the ray 
be determined, the 
emergent ray will be 
parallel to the inci¬ 


dent ray. Hence, the apparent position 
of an object viewed through a plate of 
glass is at one side of its true position. 

276. A Prism. — Let AB C (Fig. 251) 
represent a section of a glass prism 
made by a plane perpendicular to the 
refracting edge A. Also, let LI be a 



Figure 250.— Inci¬ 
dent and Emergent 
Rays Parallel. 


ray incident on the face BA. This 
ray will be refracted along IE , and 
entering the air at the point E will 
be refracted again, taking the di¬ 
rection EO. 

Reflect across the table a strong beam 
of light and intercept it with a sheet of 
green glass. Let this ribbon of green 
light be incident on a prism of small re¬ 
fracting'angle in such a manner that only part of the beam passes 
through the prism. Two lines of light may be traced through the 



Figure 251.—Path of Light 
Through Prism. 































TOTAL INTERNAL REFLECTION 


243 


dust of the room or by means of smoke. By turning the prism about 
its axis, the angle between these lines of light can be varied in size. 
It is the angle of deviation, represented by the angle D in the figure. 
The angle of deviation is least when the angles of incidence and 
emergence are equal; this occurs when the path of the ray through 
the prism is equally inclined to the two faces. 

277. Atmospheric Refraction. — Light coming to the eye 
from any heavenly body, as a star, unless it is directly 
overhead, is gradually 
bent as it passes through 
the air on account of the 
increasing density of the 
atmosphere near the 
earth’s surface. Thus, if 
S in Fig. 252 is the real 
position of a star, its ap¬ 
parent position will be S' 

, i. 77f Figure 252. — Atmospheric Refraction. 

to an observer at A. 

Such an object appears higher above the horizon than its 
real altitude. The sun rises earlier on account of atmos¬ 
pheric refraction than it otherwise would, and for the 

Twilight, the mirage of the 
desert, and the looming of 
distant objects are phenom¬ 
ena of atmospheric refraction. 

278. Total Internal Reflec¬ 
tion. — Take the apparatus of § 271 
and place the cardboard against the 
end of the jar so that the slit is near 
the bottom (Fig. 253). Reflect a 
strong beam of light up through 
the water and incident on its under 
surface just back of the center of the protractor scale. Adjust the slit 
so that the beam shall be incident at an angle a little greater than 50°. 
It will be reflected back into the water as from a plane mirror. 








244 


LIGHT 


As the angle of refraction is always greater than the 
angle of incidence when the light passes from water into 
air, it is evident that there is an incident angle of such a 
value that the corresponding angle of refraction is 90°, 
that is, the refracted light is parallel to the surface. If 
the angle of incidence is still further increased, the light 

no longer passes out into 
the air, but suffersTotaZ 
internal reflection . 

279. The Critical Angle. 
—The critical angle is the 
angle of incidence corre¬ 
sponding to an angle of 
refraction of 90°. This 

angle varies with the in- 
Figure 254. — Critical Angle. , „ . , 

dex ot retraction of the 

substance. It is about 49° for water, 42° for crown glass, 

38° for flint glass, and 24° for diamond. 

Of all the rays diverging from a point at the bottom 
of a pond and incident on the surface, only those within 
a cone whose semi-angle is 49° pass into the air. All 
those incident at a larger angle un¬ 
dergo total internal reflection (Fig. 

254). Hence, an observer under 
water sees all objects outside as if 
they were crowded into this cone; 
beyond this he sees by reflection ob¬ 
jects on the bottom of the pond. 

Total reflection in glass is shown 
by means of a prism whose cross sec¬ 
tion is a right-angled isosceles tri¬ 
angle (Fig. 255). A ray incident normally on either face 
about the right angle enters the prism without refraction, 



Figure 255. — Total Re¬ 
flection by Prism. 












QUESTIONS AND PROBLEMS 


245 


and is incident on the hypotenuse at an angle of 45°, 
which is greater than the critical angle. The ray there¬ 
fore suffers total in¬ 
ternal reflection and 
leaves the prism at 
right angles to the in- # 
cident ray. A simi- A 

lar prism is sometimes _ 

Figure 256. — Erecting Prism. 

used in a projecting 

lantern for making the image erect (Fig. 256). It would 
otherwise be inverted with respect to the object. 

Questions and Problems 

1. Why are reflectors back of wall lamps frequently made concave 
at the outer edge and convex in the central part ? 

2. Show that atmospheric refraction increases the length of 
daylight. 

3 . A plane mirror is revolved through an angle of 20°. Show by 
diagram that a ray of light incident on the mirror will be displaced 40°. 

4 . Show that the deviation of a ray of light by a glass prism is in¬ 
creased by increasing the angle of the prism. 

5 . Show that the deviation of a ray of light by a prism is increased 
by increasing the index of refraction. 

6. Why does the full moon when seen near the horizon appear just 
a little elliptical, the longer axis being horizontal? 

7 . Why does a stream of water, to one standing on its bank, appear 
less than its true depth ? 

8. A genuine diamond is distinctly visible in carbon disulphide, a 
paste or false diamond is nearly invisible. Explain. (The paste 
diamond is flint glass.) 

9. What peculiarity will the image of an object have if the mirror 
is convex cylindrical ? 

10 . In spearing a fish from a boat would you strike directly at the 
apparent position of the fish? Explain. 

11 . Show by diagram the apparent displacement of a body a,s seen 
by looking obliquely at it through a plate glass window. 










246 


LIGHT 


12. Why is powdered glass opaque ? 

13 . Show by diagram that a triangular prism of air within water 
has the opposite effect on the direction of a ray of light passing through 
it that a prism of water in air has. 


V. LENSES 

280. Kinds of Lenses. —A lens is a portion of a transpar¬ 
ent substajice bounded by two surfaces, one or both being 




curved. The curved surfaces are usually spherical (Fig. 
257). Lenses are classified as follows: 


1. Double-convex, — both surfaces convex . . 

2. Plano-convex, — one surface convex, one 

plane . 

3. Concavo-convex, — one surface convex, one 

concave . 


Converging lenses, 
> thicker at the middle 
than at the edges. 


4. 


5. 


6 . 


Double-concave, — both surfaces concave . . 

Plano-concave, — one surface concave, one 

plane . 

Convexo-concave, — one surface concave, one 
convex . 


Diverging lenses, 

► thinner at the middle 
than at the edges. 











TRACING RATS THROUGH LENSES 


247 


The concavo-convex and the convexo-concave lenses 
are frequently called meniscus lenses. The double-con¬ 
vex lens may be regarded as the type of the converging 
class of lenses, and the double-concave lens of the diverg¬ 
ing class. 

281. Definition of Terms relating to Lenses. — The centers 
of the spherical surfaces bounding a lens are the centers of 
curvature. The optical center is a point such that any ray 
passing through it and the lens suffers no change of di¬ 
rection. In lenses whose 
surfaces are of equal curv- 1 
ature, the optical center 
is their center of volume, 
as 0, in Fig. 258. In 
piano-lenses, the optical 
center is the middle point 
of the curved face. The 
straight line, CC\ through the centers of curvature, is the 
principal axis , and any other straight line through the op¬ 
tical center, as EH, is a secondary axis. The normal at 
any point of the surface is the radius of the sphere drawn 



Figure 258.- —Optical Center of Lens. 



Figure 259. — Tracing Ray through Converging Lens. 


to that point; thus CD is the normal to the surface AnB 
at D. 

282. Tracing Rays through Lenses. — A study of Figs. 
259 and 260 shows that the action of lenses on rays of 






248 


LIGHT 


light traversing them is similar to that of prisms, and 
conforms to the principle illustrated in § 276. A ray is 
always refracted toward the perpendicular on entering a 
denser medium (glass) and away from it on entering a 
medium of less optical density. Thus we see that the 
convex lens bends a ray toward the principal axis , while 
the concave lens (Fig. 260) bends it away from this axis. 



N 

Figure 260. — Tracing Ray through Diverging Lens. 


(For tracing the path of a ray geometrically, consult 
Appendix V.) 

283. The Principal Focus. — Hold a converging lens so that the 
rays of the sun fall on it parallel to its principal axis. Beyond the 
lens hold a sheet of white paper, moving it until the round spot of 
light is smallest and brightest. If held steadily, a hole may be 
burned through the paper. This spot marks the principal focus of 
the lens, and its distance from the optical center is the principal focal 
length. 

For double-convex lenses, the two faces having the 
same radius of curvature, the principal focus is at the 
center of curvature when the index of refraction is 1.5. 
If the index is greater than 1.5, the focal length is less 
than the radius of curvature; if less than 1.5, it is 
greater than this radius. 

Converging lenses are sometimes called burning glasses 
because of their power to focus the heat rays, as shown in 
the experiment. 







CONJUGATE FOCI OF LENSES 


249 


Figure 261 shows that parallel rays are made to con¬ 
verge toward the principal focus F by a converging lens, 
and the focus is 

7tr 

real; on the other 
hand, Fig. 262 illus¬ 
trates the diverging 
effect of a concave 
lens on parallel rays; 
the focus F is now 
virtual because the 
rays after passing 
through the lens only apparently come from F. In gen¬ 
eral, converging lenses increase the convergence of light, 
while diverging lenses decrease it. 


A 



h c ' n 

6 

1 


Figure 261. — Principal Focus of a 
Converging Lens. 



N 

Figure 262. — Principal Focus of a Diverging Lens.' 

284. Conjugate Foci of Lenses. — If a pencil of light di¬ 
verges from a point and is incident on th^ lens, it is 
focused at a point on the axis through the radiant point. 



JV 

Figure 263. — Conjugate Foci, Converging Lens. 












250 


LIGHT 


These points are called conjugate foci, for the same reason 
as in mirrors. 

In Fig. 263 a pencil of rays BAE diverges from A and 
is focused by the lens at the point H. It is evident that 
if the rays diverge from H\ they would be brought to a 
focus at A. Hence A and H are conjugate foci. 

285. Images by Lenses. — Place in a line on the table in a dark¬ 
ened room a lamp, a converging lens of known focal length, and a 
white screen. If, for example, the focal length of the Jens is 30 cm., 
place the lamp about *70 cm. from it, or more than twice the focal 
length, and move the screen until a clearly defined image of the lamp 
appears ou it. This image will be inverted, smaller than the object, 
and situated between 30 cm. and 60 cm. from the lens. By placing 
the lamp successively at 60 cm., 50 cm., 30 cm., and 20 cm., the images 
will differ in position and size, and in the last case will not be received 
on the screen, but may be seen by looking through the lens toward 
the lamp. If a diverging lens be used, no image can be received on 
the screen because they are all virtual. 

• 

The results of such an experiment may be summarized 
as follows : 

I. When the object is at a finite distance from a con¬ 
verging lens, and farther than twice the focal length, the 


M 



image is real, inverted, at a distance from the lens of 
more than once and less than twice the focal length, and 
smaller than the object (Fig. 264). 








IMAGES BY LENSES 


251 


IT. When the object is at a distance of twice the focal 
length from a converging lens, the image is real, inverted, 


M 



Figure 265. — Object Twice Focal Lfngth from Lens. 

at the same distance from the lens as the object, and of 
the same size (Fig. 265). 

III. When the object is at a distance from a con¬ 
verging lens of less than twice and more than once its 



Figure 266. — Object Less than Twice Focal Length from Lens. 

focal length, the image is real, inverted, at a distance of 
more than twice the focal length, and larger than the 
object (Fig. 266). 

IV. When the object is at the principal focus of a con 
verging lens, no distinct image is formed (Fig. 267). 



Figure 267. — Object at Principal Focus. 




















252 


LIGHT 


V. When the object is between a converging lens and 
its principal focus, the image is virtual, erect, and en¬ 
larged (Fig. 268). 



Figure 268 . — Object Less than Focal Length from Lens. 


VI. With a diverging lens, the image is always virtual, 
erect, and smaller than the object (Fig. 269). 

286. Graphic Construction of Images by Lenses. — The im¬ 
age of an object by a lens consists of the images of its 
points. If the object is represented by an arrow, it is 



Figure 269 . — Image Virtual in Diverging Lens. 


necessary to find only the images of its extremities. This 
is readily done by following two general directions: 

First. Draw secondary axes through the ends of the 
arrow. These represent rays that suffer no change in 
direction because they pass through the optical center 
(§ 281). 

Second. Through the ends of the arrow draw rays 
parallel to the principal axis. After leaving the lens, 
these pass through the principal focus (§ 283). 












SPHERICAL ABERRATION IN LENSES 


253 


The intersection of the two refracted rays from each 
extremity will be its image. 

To illustrate. Let AB be the object and MN the lens 
(Figs. 264-269). Rays along secondary axes through 0 
pass through the lens without any change in direction. 
The rays AD and BH, parallel to the principal axis, are 
refracted in the lens along DE and HI respectively, and 
emerge from the lens in a direction which passes through 
the principal focus F. The intersection of Aa with Ea 
is the image of A , and that of Bb with lb is the image of 
B. Other rays from A and B also pass through a and b 
respectively, and therefore ab is the image of AB. The 
image is virtual when the intersection of the refracted 
rays is on the same side of the lens as the object. The 
relative size of object and image is the same as their rela¬ 
tive distance from the lens. 

287. Spherical Aberration in Lenses. — If rays from any 
point be drawn to different parts of a lens, and their 


in¬ 



directions be determined after refraction, it will be found 
that those incident near the edge of the lens cross the 
principal axis, after emerging, nearer the lens than those 
incident near the middle (Fig. 270). The principal focal 
length for the marginal rays is therefore less than for 
central rays. This indefiniteness of focus is called spherical 
aberration by refraction , the effect of which is to lessen the 




254 


LIGHT 


distinctness of images formed by the lens. In practice a 
round screen, called a diaphragm , is used to cut off the 
marginal rays ; this renders the image sharper in outline, 
but less bright. In the large lenses used in telescopes the 
curvature of the lens is made less toward the edge, so that 
all parallel rays are brought to the same focus. 

288. Formula for Lenses. — The triangles AOK and aOL in 

Fig. 271 are similar. Hence, If the lens is thin, a straight 

aL LG 

line connecting D and H will pass very nearly through the optical 



center 0. Then DFO is a triangle similar to aFL, and = 01-• 

8 aL LF 

Since DO is equal to AK, the first members of the two equations 

KO O P 

above are equal to each other, and therefore ^ Put KO =p, 

LO — q, and OF = f. Then LF = q —f, and 

£ = _JL. 

9 <l~f 

Clearing of fractions and dividing through by pqf, we have 

4= - + -.(Equation 32) 

f P 9 

By measuring p and q we may compute /. For diverging lenses 
/ and q are negative. 


Questions and Problems 

1. How can a convex lens be distinguished from a concave one? 

2. Why does common window glass often give distorted images of 
objects viewed through it? 












THE MAGNIFYING GLASS 


255 


3 . How can the principal focal length of a concave spherical mirror 
be found? 

4 . Given a collection of spectacle lenses; select the concave from 
the convex. 

5 . Why do so many cheap mirrors give distorted images ? 

6. If an oarsman sticks his oar into the water obliquely, why does 
it appear broken at the point of entrance ? 

7 . Concave spherical mirrors are often mounted in frames to be 
used as hand glasses. Such mirrors are usually made by silvering one 
face of a lens. Why can several images be seen in such a mirror? 

8. When is the distance between the object and its real image as 
formed by a converging lens the least possible ? 

9 . The focal length of a camera lens is two inches. How far must 
the sensitized plate be from the lens, when the object is distant 100 ft. ? 

10 . If a reading glass has a focal length of 16 in. and in its use is 
held 10 in. from the book, what is the position of the virtual image? 

11 . An object 100 cm. in front of a converging lens gives an image 
25 cm. back of the lens. What is the focal length of the lens? 

12 . Show by diagram what effect it has on the image of an object 
by a diverging lens to move it farther aw r ay from the lens. 

13 . Why is a convex mirror used on an automobile to view objects 
back of the driver, instead of a plane mirror? 

14 . In a diverging lens, show that a pencil of light that converges 
to a point beyond the focus of the lens issues as a diverging pencil. 

15 . Where must a diverging lens be placed to render parallel a 
converging pencil of light? 

VI. OPTICAL INSTRUMENTS 

289. The Magnifying Glass, or simple microscope , is a 
double-convex lens, usually of short focal length. The 
object must be placed nearer the lens than its principal 
focus. The image is^ then virtual^ erect, and enlarged. 
If AB is* the object in Fig. 272, the virtual image is ab ; 
and if the eye be placed near the lens on the side opposite 



256 


LIGHT 


the object the virtual image will be seen in the position of 
the intersection of the rays produced, as at ab. 



290. The Compound Microscope (Fig. 273) is an instru¬ 
ment designed to obtain a greatly enlarged image of very 
small objects. In its simplest form it consists of a con¬ 
verging lens MN (Fig. 274), 
called the object glass or ob¬ 
jective, and another con¬ 
verging lens RS, called the 
eye-piece. The two lenses 
are mounted in the ends of 
the tube of Fig. 273. The 
object is placed on the stage 
just under the objective, and 
a little beyond its principal 
focus. A real image ab 
(Fig. 274) is formed slightly 
nearer the eye-piece than its 
focal length. This image 
formed b}^ the objective is 
Figure 273. — Microscope. viewed by the eyepiece, and 
the latter gives an enlarged 
virtual image. (Why?) Both the objective and the 
eyepiece produce magnification. 








THE ASTRONOMICAL TELESCOPE 


257 


291. The Astronomical Telescope. — The system of lenses 
in the refracting astronomical telescope (Fig. 275) is simi¬ 
lar to that of the compound microscope. Since it is in¬ 
tended to view distant objects, the objective MN is of 



Figure 274. — Tracing Rays to Form Image 


large aperture and long focal length. The real image 
given by it is the object for the eyepiece, which again 
forms a virtual image for the eye of the observer. The 
magnification is the ratio of the focal lengths of the objec¬ 
tive and the eyepiece. The objective must be large, for 
the purpose of collecting enough light to permit large 



magnification of the image without too great loss in 
brightness. 

Figure 275 shows that the image in the astronomical 
telescope is inverted. In a terrestrial telescope the image 
is made erect by introducing near the eyepiece two double- 
convex lenses, in such relation to each other and to the 
first image that a second real image is formed like the first, 
but erect. 

















258 


LIGHT 


292. Galileo’s Telescope. — The earliest form of telescope 
was invented by Galileo. It produces an erect image by 
the use of a diverging lens for the eyepiece (Fig. 276). 
This lens is placed between the objective and the real 
image, ab , which would be formed by the objective if the 
eyepiece were not interposed. Its focus is practically at 
the image ab, and the rays of light issue from it slightly 



divergent for distant objects. The image .is therefore at 
A!B' instead of at ab , and it is erect and enlarged. This 
telescope is much shorter than the astronomical telescope, 
for the distance between the lenses is the difference of 
their focal lengths instead of their sum. In the opera 
glass two of Galileo’s telescopes are attached together 
with their axes parallel. 

293. The Projection Lantern is an apparatus by which a 
greatly enlarged image of an object can be projected on a 
screen. The three essentials of a projection lantern are 
a strong light, a condenser, and an objective. The light 
may be the electric arc light, as shown in Fig. 277, the 
calcium light, or a large oil burner. The condenser E is 
composed of a pair of converging lenses; its chief pur¬ 
pose is the collection of the light on the object by refrac¬ 
tion, so as to bring as much as possible on the screen. 
The object AB , commonly a drawing or a photograph 








Moving Picture Film. 

Most moving picture cameras take from 16 to 120 pictures per second. 

















































* 






























* 
































































t 










































































































' 












ii 










































. 































































THE EYE 


259 


on glass, is placed near the condenser SS, where it is 
strongly illuminated. The objective, ME, is a combina¬ 
tion of lenses, acting as a single lens to project on the 
screen a real, inverted, and enlarged image of the object. 



294. The Photographer’s Camera consists of a box BO 
(Fig. 278), adjustable in length, blackened inside, and 
provided at one end with a lens or a combination of lenses, 
acting as a single one, and at the other with a holder for 
the sensitized plate. If by means of a rack and pinion the 
lens U be properly 
focused for an ob¬ 
ject in front of it, 
an inverted image 
will be formed on 
the sensitized plate 
B. The light acts 
on the salts con¬ 
tained in the sensitized film, producing in them a modifi¬ 
cation which, by the processes of “developing” and “fix¬ 
ing,” becomes a permanent negative picture of the object. 
When a “ print ” is made from this negative, the result is 
a positive picture. 

295. The Eye.—The eye is like a small photographic 
camera, with a converging lens, a dark chamber, and a 



Figure 278.-—-Camera. 



























260 


LIGHT 


sensitive screen. Figure 279 is a vertical section through 
the axis. The outer covering, or sclerotic coat H, is a 
thick opaque substance, except in front, where it is ex¬ 
tended as a transparent coat, called the cornea A. Behind 


the cornea is a dia¬ 
phragm D , consti¬ 
tuting the colored 
part of the eye, or 
the iris. The cir¬ 
cular opening in the 
iris is the pupil , 
the size of which 
changes with the 
intensity of light. 
Supported from the 
walls of the eye, 





Figure 279 . — Section of Eye. 


just back of the iris, is the crystalline lens E, a transparent 
body dividing the eye into two chambers; the anterior 
chamber between the cornea and the crystalline lens is a 
transparent fluid called the aqueous humor , while the large 
chamber behind the lens is filled with a jellylike substance 
called the vitreous humor. The choroid coat lines the walls 
of this posterior chamber, and on it is spread the retina , a 
membrane traversed by a network of nerves, branching 
from the optic nerve M. The choroid coat is filled with a 
black pigment, which serves to darken the cavity of the 
eye, and to absorb the light reflected internally. 

296. Sight. —When rays of light diverge from the ob¬ 
ject and enter the pupil of the eye they form an inverted 
image on the retina (Fig. 280) precisely as in the photo¬ 
graphic camera. In place of the sensitized plate is the 
sensitive retina, from which the stimulus is carried to the 
brain along the optic nerve. 









THE BLIND SPOT 


261 


In the camera the distance between the lens and the 
screen or plate must be adjusted for objects at different 
distances. In the eye the corresponding distance is fixed, 
and the adjustment for distinct vision is made by uncon¬ 
sciously changing the curvature of the front surface of 



the crystalline lens by means of the ciliary muscle JP, 6r 
(Fig. 279). This capability of the lens of the eye to 
change its focal length for objects at different distances 
is called accommodation. 

297. The Blind Spot.—There is a small depression where 
the optic nerve enters the eye. The rest of the retina is 
covered with microscopic rods and cones, but there are 
none in this depression, and it is insensible to light. It is 

* • 

Figure 281.— To Find Blind Spot. 

accordingly called the blind spot. Its existence can be 
readily proved by the help of Fig. 281. Hold the book 
with the circle opposite the right eye. Now close the left 
eye and turn the right to look at the cross. Move the 
book toward the eye from a distance of about a foot, and 
a position will readily be found where the black circle 
will disappear. Its image then falls on the blind spot. 
It may be brought into view again by moving the book 
either nearer the eye or farther away. 








262 


LIGHT 


298. The Prism Binocular. — While the opera glass 
(§ 292) is compact and gives an erect image, it has only 
a small field of view, and is usually made to magnify only 
three or four times. For the purpose of obtaining a 
larger field of view with equal compactness, the prism 

binocular has been devised. 

The desired length has been 

obtained by the use of two 

total reflecting prisms (Fig. 

282), by means of which 

the light is reflected forward 

and back again in the tube. 

Not only is compactness 

„ „ secured in this manner, but 

Figure 282. — Prism Binocular. 

the reflections in the prisms 
increase the focal length of the objective and serve to give 
an erect image without “ perversion.” 

299. Defects of the Eye. — A normal eye in its passive or 
relaxed condition focuses parallel rays on the retina. The 
defects of most frequent occurrence are ne ar-sightedne ss, 
far-sightedness, and astigmatism. 

If the relaxed eye focuses parallel rays in front of the 
retina (Fig. 288), it is near-sighted. The length of the 
eyeball from front to back 
is then too great for the 
focal length of the crys¬ 
talline lens. The correc¬ 
tion consists in placing in 
front of the eye a diverg¬ 
ing lens that makes with the lens of the eye a less con¬ 
vergent system than the crystalline lens itself. If the 
focal length of the diverging lens is equal to the greatest 
distance of distinct vision for the near-sighted eye, and if 



Figure 283.- —Near-sightedness. 












ANALYSIS OF WHITE LIGHT 


263 



Figure 284. — Far-sightedness. 


this lens is held close to the eye, parallel rays from a dis¬ 
tant object will enter the eye as if they came from the 
principal focus of the lens, the image falls on the retina, 
and vision is made distinct. 

If the relaxed eye focuses parallel rays from distant 
objects behind the retina, it is far-sighted. The length of 
the eyeball is then too short to correspond with the focal 
length of the crystalline 
lens. The correction con¬ 
sists in placing in front of 
the eye a converging lens 
(Fig. 284), making with 
the lens of the eye a more 
converging system than the eye lens alone. Light from 
a near object then enters the eye as if it came from a dis¬ 
tant one and vision becomes distinct. 

Sometimes the front of the cornea has different curva¬ 
tures in different planes through the axis; that is, it has 
a somewhat cylindrical form. Persons with such an eye 
do not see with equal distinctness all the figures on the 
face of a watch. This defect is known as astigmatism. 
It is corrected by the use of a lens, one surface of which 
at least is not spherical but differs from it in the opposite 
sense to that of the defective eye. The astigmatism of 
the two eyes is not usually the same. 


VII. DISPERSION 

300. Analysis of White Light. The Solar Spectrum. — 

Darken the room, and by means of a mirror hinged outside the window, 
reflect a pencil of sunlight into the room. • Close the opening in the 
window with a piece of tin, in which is cut a very narrow vertical slit. 
Let the ribbon of sunlight issuing from the slit be incident obliquely 
on a glass prism (Fig. 285). A many-colored band, gradually chang¬ 
ing from red at one end through orange, yellow, green, blue, to violet 






264 


LIGHT 


at the other, appears on the screen. If a converging lens of about 30 
cm. focal length be used to focus an image of the slit on the screen, 
and the prism be placed near the principal focus, the colored images 

of the slit will be 
more distinct. 

This experi¬ 
ment shows that 
white or colorless 
light is a mix¬ 
ture of an infinite 
number of differ¬ 
ently colored 
rays, of which 
the red is re¬ 
fracted least and 
the violet most. 
The brilliant band of light consists of an indefinite num¬ 
ber of colored images of the slit; it is called the solar 
spectrum , and the opening out or separating of the beam 
of white light is known as dispersion. 

301. Synthesis of Light. —Project a spectrum of sunlight on the 
screen. Now place a second prism like the first behind it, but re¬ 
versed in position (Fig. 286). There 
will be formed a colorless image, 
slightly displaced on the screen. 

The second prism reunites the 
colored rays, making the effect 
that of a thick plate of glass (§ 275). The recomposition 
of the colored rays into white light may also be effected by- 
receiving them on a concave mirror or a large convex lens. 

302. Chromatic Aberration. — Let a beam of sunlight into the 
darkened room through a round hole in a piece of cardboard. Pro- 



Figure 286. — Reforming 
White Light. 










THE ACHROMATIC LENS 


265 



Figure 287. — Chromatic 
Aberration. 


ject an image of this aperture on the screen, using a d< >uble-convex 
lens for the purpose. The round image will be bordered with the 
spectral colors. 

This experiment shows that the, lens refracts the rays 
of different colors to different foci. Tliis defect in lenses 
is known as chromatic aberration. 

The violet rays, being more re¬ 
frangible than the red, will have 
their focus nearer to the lens than 
the red, as shown in Fig. 287, 
where v is the principal focus for 
violet light and r for red. If a 
screen were placed at #, the image would be bordered 
with red, and if at y with violet. 

303. The Achromatic Lens. — With a prism of crown glass pro¬ 
ject a spectrum of sunlight on the screen, and note the length of the 
spectrum when the prism is turned to give the least deviation (§ 276). 
Repeat the experiment with a prism of flint glass having the same re¬ 
fracting angle. The spectrum formed by the flint glass will be about 
twice as long as that given by crown glass, while the position of the 
middle of the spectrum on the screen is about the same in the two 
cases. Now use a flint glass prism whose refracting angle is half that 
of the crown glass one. The spectrum is nearly equal in length to 

that given by the crown 
IF glass prism, but the devia¬ 

tion of the middle of it is 
considerably less. Finally, 
place this flint glass prism 
in a reversed position 

„ against the crown glass one 

Figure 288.-Achromatic Prism. (Hg> 288 >. The image o£ 

the aperture is no longer colored, and the deviation is about half that 
produced by the crown glass alone. 

In 1757 Dollond, an English optician, combined a double- 
convex lens of crown glass with a plano-concave lens of 










266 


LIGHT 


flint glass so that the dispersion by the one neutralized 
that due to the other, while the refraction was reduced 
about half (Fig. 289). Such a lens or system 
of lenses is called achromatic , since images 
formed by it are not fringed with the spectral 
colors. 

304. The Rainbow .—Cement a crystallizing beaker 
Figure 289. 12 or 15 cm. in diameter to a slate slab. Fill the beaker 
Lens HR ° MATIC wa * er through a hole drilled in the slate. Sup¬ 

port the slate in a vertical plane and direct a ribbon 
of white light upon the beaker at a point about 60° above its hori¬ 
zontal axis, as SA (Fig. 290). The light may be traced through the 
water, part of it issuing at the back at B as a diverging pencil, and 
a part reflected to C and issuing as spectrum colors along CD. If 
other points of incidence be tried, the colors given by the reflected 
portion are very indistinct except at 70° below the axis. After re¬ 
fraction at this point, 
the light can be traced 
through the water, is¬ 
suing as spectral colors 
after having suffered 
two refractions and 
two reflections. 

The experiment 
shows that the light 
must be incident at 
definite angles to 
give color effects. The red constituent of white light in¬ 
cident at about 60° keeps together after reflection and 
subsequent refraction; that is, the red rays are practically 
parallel and thus have sufficient intensity to produce a 
red image. The same is true of the violet light incident 
at about 59° from the axis. The other spectral colors ar¬ 
range themselves in order between the red and violet. 

For light incident at about 70° from the axis a similar 



Figure 290. — Illustrating Rainbow. 










DISCONTINUOUS SPECTRA 


267 


spectrum band is formed by light which has suffered two 
refractions and two reflections. 

So when sunlight falls on raindrops the light is dispersed 
and a rainbow is formed. Two bows are often visible, the 
primary and the secondary. The primary is the inner and 
brighter one, formed b} T a single internal reflection. It is 
distinguished by hav- 
ing the red on the out- s 1 '- 
side and the violet on f 
the inside. The sec¬ 
ondary bow, formed 
by two internal reflec¬ 
tions, is fainter, and 

s - 

has the order of colors 
reversed. Figure 291 

,, Figure 291.— Primary and Secondary Bows. 

shows the relative po- . 

sitions of the sun, the observer, and the raindrops which 
form the bows. It should be noted that all drops in the 
line vE send violet light to the eye, those along rE send 
red light, and those between the two send the intermediate 
colors. 

305. Continuous Spectra. —Throw on a screen the spectrum of 
the electric arc, using preferably for the purpose a hollow prism filled 
with carbon bisulphide. The spectrum will be composed of colors 
from red at one end through orange, yellow, green, blue, and violet 
at the other without interruptions or gaps. 

The experiment illustrates continuous spectra, that is, 
spectra without breaks or gaps in the color band. Solids, 
liquids , and dense vapors and gases, when heated to incan¬ 
descence, give continuous spectra. 

306. Discontinuous Spectra. — Project on the screen the spectrum 
of the electric light. Place in the arc a few crystals of sodium nitrate, 








268 


LIGHT 


The intense heat will vaporize the sodium, and a spectrum will be 
obtained consisting of bright colored lines, one red, one yellow, three 
green, and one violet, the yellow being most prominent. 

The experiment illustrates discontinuous or bright line 
spectra , that is, spectra consisting of one or more bright 
lines of color separated by dark spaces. Rarefied gases 
and vapors , when heated to incandescence , give discontinuous 
spectra. 


_ 


307. Absorption Spectra. — Project on the screen the spectrum 
of the electric light. Between the lamp and the slit S (Fig. 292) 

vaporize metallic so¬ 
dium in an iron 
spoon so placed that 
the white light passes 
through the heated 
sodium vapor before 
dispersion by the 
prism. A dark line 
will appear on the 
screen in the yellow 
of the spectrum at 
the place where the 
bright line was ob¬ 
tained in the preced¬ 
ing experiment. 



Figure 292.—Absorption Spectrum. 


The experiment illustrates an absorption , reversed or dark 
line spectrum. The dark line is produced by the absorption 
of the yellow light by sodium vapor. Gases and vapors 
absorb light of the same refrangibility as they emit at a 
higher temperature. 


308. The Fraunhofer Lines. — Show on the screen a carefully 
focused spectrum of sunlight. Several of the colors will appear 
crossed with fine dark lines (Fig. 293). 

Fraunhofer was the first to notice that some of these 
lines coincide in position with the bright lines of certain 


















THE SPECTROSCOPE 


269 


I 


Red Orange Yellow Green Blue Indigo Violet 

Figure 293.— Fraunhofer Lines. 
these lines has been found to be 


artificial lights. He mapped no less than 576 of them, 
and designated the more important ones by the letters 

A , B, C, D , F, F , 6r, H, the first in the extreme red and 
the last in the vio- 

let. For th is reason 
they are referred to 
as the Fraunhofer 
lines. In recent 
years the number of 
practically unlimited. 

In the last experiment it was shown that sodium vapor 
absorbs that part of the light of the electric arc which is 
of the same refrangibility as the light emitted by the 
vapor itself. Similar experiments with other substances 
show that every substance has its own absorption spec¬ 
trum. These facts suggested the following explanation 
of the Fraunhofer lines : The heated nucleus of the sun 
gives off light of all degrees of refrangibility. Its spec¬ 
trum would therefore be continuous, were it not sur¬ 
rounded by an atmosphere of metallic vapors and of gases, 
which absorb or weaken those rays of which the spectra 
of these vapors consist. Hence, the parts of the spec¬ 
trum which would have been illuminated by those par¬ 
ticular rays have their brightness diminished, since the 
rays from the nucleus are absorbed, and the illumination 
is due to the less intense light coming from the vapors. 
These absorption lines are not lines of no light, but are 
lines of diminished brightness, appearing dark by contrast 
with the other parts of the spectrum. 

309. The Spectroscope. —The commonest instrument for 
viewing spectra is the spectroscope (Fig. 294). In one 
of its simplest forms it consists of a prism A , a telescope 

B , and a tube called the collimator C, carrying an adjust- 









































270 


LIGHT 



able slit at the outer end D , and a converging lens at the 
other E, to render parallel the diverging rays coming from 


Figure 294. — Spectroscope. 


the slit. The slit must therefore be placed at the princi¬ 
pal focus of the converging lens. To mark the deviation 
of the spectral lines, there is provided on the supporting 


Figure 295. — Iron Vapor in the Sun. 

table a divided circle JF, which is read by the aid of 
verniers and reading microscopes attached to the tele¬ 
scope arm. 

The applications of the spectroscope are many and various. By 
an examination of their absorption spectra, normal and diseased blood 

















VARIOUS SPECTRA 










































COLOR OF OPAQUE BODIES 


271 


are easily distinguished, the adulteration of substances is detected, 
and the chemistry of the stars is approximately determined. Figure 
295 shows the agreement of a number of the spectral lines of iron 
with Fraunhofer lines in the solar spectrum; they indicate the pres¬ 
ence of iron vapor in the atmosphere of the sun. 


VIII. COLOR 


310. The Wave Length of light determines its color. 
Extreme red is produced by the longest waves, and ex¬ 
treme violet by the shortest. The following are the wave 
lengths for the principal Fraunhofer lines in air at 20° C. 
and 760 mm. pressure : 


A Dark Red 
B Red . . 
C Orange . 
D x Yellow . 
D, ... . 


0.0007621 mm. 
6884 mm. 
6563 mm. 
5896 mm. 
5890 mm. 


E x Light Green 

. 

F Blue . . . 
G Indigo . . 
H x Violet . . 


0.0005270 mm. 
5269 mm. 
4861 mm. 
4293 mm. 
3968 mm. 


In white light the number of colors is infinite, and they 
pass into one another by imperceptible gradations of shade 
and wave length. Color stands related to light in the 
same way that pitch does to sound. In most artificial 
lights certain colors are either feeble or wanting. Hence, 
artificial lights are not generally white, but each one is 
characterized by the color that predominates in its 
spectrum. 


311. Color of Opaque Bodies. —Project the solar spectrum on a 
white screen. Hold pieces of colored paper or cloth successively in 
different parts of the spectrum. A strip of red flannel appears bril¬ 
liantly red in the red part of the spectrum, and black elsewhere; a 
blue ribbon is blue only in the blue part of the spectrum, and a piece 
of black paper is black in every part of the spectrum. 

The experiment shows that the color of a body is due both 
to the light that it receives and the light that it reflects ; 





272 


LIGHT 


that a body is red because it reflects chiefly, if not wholly, 
the red rays of the light incident upon it, the others being 
absorbed wholly or partly at its surface. It cannot be red 
if there is no red light incident upon it. In the same way 
a body is white if it reflects all the rays in about equal 
proportions, provided white light is incident upon it. So 
it appears that bodies have no color of their own, since 
they exhibit no color not already present in the light 
which illuminates them. 

This truth is illustrated by the difficulty experienced in 
matching colors by artificial lights, and by the changes in 
shades some fabrics undergo when taken from sunlight into 
gaslight. Most artificial lights are deficient in blue and 
violet rays; and hence all complex colors, into which blue 
or violet enters, as purple and pink, change their shade 
when viewed by artificial light, 

312. Color of Transparent Bodies. — Throw the spectrum of 
the sun or of the arc light on the screen. Hold across the slit a flat 
bottle or cell filled with a solution of ammoniated oxide of copper. 1 
The spectrum below the green will be cut off. Substitute a solution 
of picric acid, and the spectrum above the green will be cut off. Place 
both solutions across the slit and the green alone remains. It is the 
only color transmitted by both solutions. In like manner, blue glass 
cuts off the less refrangible part of the spectrum, ruby glass cuts off 
the more refrangible, and the two together cut off the whole. 

This experiment shows that the color of a transparent 
body is determined by the colors that it absorbs. It is 
colorless like glass if it absorbs all colors in like proportion, 
or absorbs none; but if it absorbs some colors more than 
others, its color is due to the mixed impression produced 
by the various colors passing through it. 

1 It is prepared by adding ammonia to a solution of copper sulphate, 
until the precipitate at first formed is dissolved. 



THREE PRIMARY COLORS 


273 


313. Mixing 1 Colored Lights. — Out of colored papers cut several 
disks, about 15 cm. in diameter, with a hole at the center for mounting 
them on the spindle of a whirling machine 
(Fig. 296), or for slipping them over the 
handle of a heavy spinning top. Slit them 
along a radius from the circumference to 
the center, so that two or more of them 
can be placed together, exposing any pro¬ 
portional part of each one as desired (Fig. 

297). Select seven disks, whose colors most 
nearly represent those of the solar spec¬ 
trum ; put them together so that equal por¬ 
tions of the colors are exposed. Clamp on 
the spindle of the whirling machine and 
rotate them rapidly. When viewed in a 
strong light the color is an impure white 
or gray. 

This method of mixing colors is 
based on the physiological fact that 
a sensation lasts longer than the 
stimulus producing it. Before the sensation caused by one 
stimulus has ceased, the disk has moved, so that a different 
impression is produced. The effect is equivalent to 
superposing the several colors on one 
another at the same time. 

314. Three Primary Colors. — If red, 
green, and blue, or violet disks are 
Figure 297. —Colored usec ^ as i n g 313, exposing equal por¬ 
tions, gray or impure white is ob¬ 
tained when they are rapidly rotated. If any two colors 
standing opposite each other in Fig. 298 are used, the re¬ 
sult is white; and if any two alternate ones are used, the 
result is the intermediate one. By using the red, the 
green, and the violet disks, and exposing in different pro¬ 
portions, it has been found possible to produce any color 




Figure 296. — Mixing 
Colored Lights. 







274 


LIGHT 


Purple 



uaaj,*) 

Figure 298.— Color Disk. 


of the spectrum. This fact suggested to Dr. Young the 
theory that there are only three primary color sensations, 
and that our recognition of different colors is due to the 
excitation of these three in vary¬ 
ing degrees. 

The color top is a standard 
toy provided with colored paper 
disks, like those of Fig. 296. 
When red, green, and blue disks 
are combined so as to show sec¬ 
tors of equal size, the top, when 
spinning in a strong light, ap¬ 
pears to be gray. Gray is a 
white of low intensity. The 
colors of the disks are those of pigments, and they are not 
pure red, green, and blue. 

315. Three- and Four-color Printing. — The frontispiece 
of this book illustrates a four-color print of much interest. 
Such a print is made up of very fine lines and dots of the 
four pigments, red, yellow, blue, and black. The various 
colors in the picture are mixtures of these four with the 
white of the paper. 

The picture is made by printing the four colors one on 
top of the other from four copper plates, each of which 
represents only that part of the picture where a certain 
color must be used to give the proper final effect. These 
plates are made from four negatives. The process of pre¬ 
paring these negatives is as follows : 

Each negative is made by taking a picture of the origi¬ 
nal colored drawing through a colored “ filter,” which cuts 
out all the colors except the one desired. A blue filter is 
used to prepare the plate that prints with yellow ink, a 
green filter to prepare the red printing plate, a red filter 




MIXING PIGMENTS 


275 


for the blue printing plate, and a chrome yellow filter for 
the black printing plate. 

A cross-lined glass screen, dividing the image into small 
dots, is placed in front of the negatives in the camera. 
Glue enamel prints are then made on copper, and the plates 
are etched, leaving the desired pri ting surface in relief. 

In the frontispiece the yellow is printed first, the red 
over the yellow second, the blue third over the yellow and 
red, and the black last over the yellow, red, and blue. 

When no black is used the process is known as the 
three-color process . 

316. Complei entary Colors .—Any two colors whose mix¬ 
ture produces on the eye the impression of white light are 
called complementary. Thus, red and bluish green are 
complementary; also orange and light blue. When 
complementary colors are viewed next to each other, the 
effect is a mutual heightening of color impressions. 

Complementary colors may be seen by what is known as retinal 
fatigue. Cut some design out of paper, and paste it on red glass. 
Project it on a screen in a dark room. Look steadily at the screen 
for several seconds, and then turn up the lights. The design will 
appear on a pale green ground. 

This experiment shows that the portion of the retina 
on which the red light falls becomes tired of red, and 
refuses to convey as vivid a sensation of red as of the 
other colors, when less intense white light is thrown on 
it. But it retains its sensitiveness in full for the rest of 
white light, and therefore conveys to the brain the im¬ 
pression of white light with the red cut out; that is, of 
the complementary color, green. 

317. Mixing Pigments. — Draw a broad line on the blackboard 
with a yellow crayon. Over this draw a similar band with a blue 
crayon. The result will be a band distinctly green. 


276 


LIGHT 


The yellow crayon reflects green light as well as yel¬ 
low, and absorbs all the other colors. The blue crayon 
reflects green light along with the blue, absorbing all 
the others. Hence, in superposing the two chalk marks, 
the mixture absorbs all but the green. The mark on the 
board is green, because that is the only color that sur¬ 
vives the double absorption. In mixing pigments, the 
resulting color is the residue of a process of successive 
absorptions. If the spectral colors, blue and yellow, are 
mixed, the product is white instead of green. So we see 
that a mixture of colored lights is a very different thing 
from a mixture of pigments. 

IX. INTERFERENCE AND DIFFRACTION 

318. Newton’s Rings. — Press together at their center two small 
pieces of heavy plate glass, using a small iron clamp for the purpose. 
Then look obliquely at the glass; curved bands of color may be seen 
surrounding the point of greatest pressure. 

This experiment is like one performed by Newton 
while attempting to determine the relation between the 
colors in the soap bubble and the thickness of the film. 
He used a plano-convex lens of long focus resting on a 
plate of plane glass. Figure 299 
shows a section of the apparatus. 
Between the lens and the plate 
Figure 299. —Newtons there is a wedge-shaped film of 
air, very thin, and quite similar to 
that formed between the glass plates in the above experi¬ 
ment. If the glasses are viewed by reflected light, there 
is a dark spot at the point of contact, surrounded by sev¬ 
eral colored rings (Fig. 300) ; but if viewed by trans¬ 
mitted light, the colors are complementary to those seen 
by reflection (§ 316). 







NEWTON'S RINGS 


277 


The explanation is to be found in the interference of 
two sets of waves, one reflected internally from the 
curved surface ACB , and the other from the surface 
B CE on which it presses. If light 
of one color is incident on AB , a 
portion will be reflected from A CB, 
and another portion from DCE. 

Since the light reflected from BCE 
has traveled farther by twice the 
thickness of the air film than that 
from ACB , and the film gradually 
increases in thickness from C out¬ 
ward, it follows that at some places Figure 300. — Colored 
.. n i Rings. 

the two reflected portions will meet 

in like phase, and at others in opposite phase, causing a 
strengthening of the light at the former, and extinction 
of it at the latter. 

If red light be used, the appearance will be that of a 
series of concentric circular red bands separated by dark 
ones, each shading off into the other. If violet light be 
employed, the colored bands will be closer together on 
account of the shorter wave length. Other colors will 
give bands intermediate in diameter between the red 
and violet. From this it follows that if the glasses be 
illuminated by white light, at every point some one color 
will be destroyed. The other colors will be either weak¬ 
ened or strengthened, depending on the thickness of the 
air film at the point under consideration, the color at 
each point being the result of mixing a large number of 
colors in unequal proportions. Hence, the point C will 
be surrounded by a series of colored bands. 1 

1 The light from ACB differs in phase half a wave length from that 
reflected from DE, because the former is reflected in an optically dense 




278 


LIGHT 


The colors of the soap bubble, of oil on water, of heated 
metals which easily oxidize, of a thin film of varnish, and 
of the surface of very old glass, are all caused by the in¬ 
terference of light reflected from the two surfaces of a 
very thin film. 

319. Diffraction. — Place two superposed pieces of perforated 
cardboard in front of the condenser of the projection lantern. The 
projected images of the very small holes, as one piece is moved across 
the other, are fringed with the spectral colors. 

With a fine diamond point rule a number of equidistant parallel 
lines very close together on glass. They compose a transparent dif¬ 
fraction grating. Substitute this for the prism in projecting the spec¬ 
trum of sunlight or of the arc light on the screen (§ 300). There 
will be seen on the screen a central image of the slit, and on either 
side of it a series of spectra. Cover half of the length of the slit with 
red glass and the other half with blue. There will now be a series 
of red images and also a series of blue ones, the red ones being far¬ 
ther apart than the blue. Lines ruled close together on smoked 
glass may be used instead of a “grating.” 

These experiments illustrate a phenomenon known as 
diffraction . The colored bands are caused by the inter¬ 
ference of the waves of light which are propagated in all 
directions from the fine openings. The effects are visible 
because the transparent spaces are so small that the inten¬ 
sity of the direct light from the source is largely re¬ 
duced. Diffraction gratings are also made to operate by 
reflecting light. Striated surfaces, like mother-of-pearl, 
changeable silk, and the plumage of many birds, owe 
their beautiful changing colors to interference of light by 
diffraction. 


medium next to a rare one, and the latter in an optically rare medium 
next to a dense one. This phase difference is additional to the one above 
described. 



QUESTIONS 


279 


Questions 

1. How many degrees is it from the sun to the highest point of the 
primary rainbow ? 

2. Why is the red on the outside of the primary bow and on the 
inside of the secondary bow ? 

3. If there are but three primary sensations, red, green, and violet, 
what effect would it have on a person’s vision if the nerves for red 
sensations were inoperative ? 

4. Why is the secondary rainbow less bright than the primary 
bow? 

5. Are the two images of an object as formed on the retina of the 
two eyes identical ? Explain. 

6 . Account for the crossed bands of light seen by looking through 
the wire screening of the window at the full moon. 

7. Account for the change in color of aniline purple when viewed 
by the light of a common kerosene lamp. 

8. Under what conditions could a rainbow be seen at midday? 

9. Account for the colors on water when gasoline is poured on it. 

10 . Why does each person in using a microscope have to focus for 

his own eyes ? 


CHAPTER IX 


HEAT 

I. HEAT AND TEMPERATURE 

320. Nature of Heat. —For a long time it was believed 
that heat was a subtle and weightless fluid that entered 
bodies and possibly combined with them. This fluid was 
called caloric. About the beginning of the last century 
some experiments of Count Rumford in boring brass can¬ 
non, and those of Sir Humphry Davy in melting two pieces 
of ice at freezing temperature by the friction of one piece 
on the other demonstrated that the caloric theory of heat 
was no longer tenable; and finally about the middle of 
the century, when Joule proved that a definite amount of 
mechanical work is equivalent to a definite amount of 
heat, it became evident that heat is a form of molecular 
energy. 

The modern kinetic theory, briefly stated, is as follows: 
The molecules of a body have a certain amount of inde¬ 
pendent motion, generally very irregular. Any increase 
in the energy of this motion shows itself in additional 
warmth, and any decrease by the cooling of the body. 
The heating or the cooling of a body, by whatever 
process, is but the transference or the transformation of 
energy. 

321. Temperature. — If We place a mass of hot iron in 
contact with a mass of cold iron, the latter becomes warmer 
and the former cooler, the heat flowing from the hot body 

280 


MEASURING TEMPERATURE 


281 


to the cold one. The two bodies are said to differ in tem - 
perature or “heat level,” and when they are brought in 
contact there is a flow of heat from the one of higher tem¬ 
perature to the one of lower until thermal (heat) equilib¬ 
rium is established. 

Temperature is the thermal condition of a body which 
determines the transfer of heat between it and any body 
in contact with it. This transfer is always from the body 
of higher temperature to the one of lower. Temperature 
is a measure of the degree of hotness; it depends solely on 
the kinetic energy of the molecules of the body. 

Temperature must be distinguished from quantity of 
heat. The water in a pint cup may be at a much higher 
temperature than the water in a lake, yet the latter con¬ 
tains a vastly greater quantity of heat, owing to the 
greater quantity of water. 

322. Measuring Temperature. — Fill three basins with mod¬ 
erately hot water, cold water, and tepid water respectively. Hold one 
hand in the first, and the other in the second for a short time; then 
transfer both quickly to the tepid water. It will feel cold to the 
hand that has been in hot water and warm to the other. Hold the 
hand successively against a number of the various objects in the room, 
at about the same height from the floor. Metal, slate, or stone ob¬ 
jects will feel colder than those of wood, even when side by side and 
of the same temperature. 

These experiments show that the sense of touch does 
not give accurate information regarding the relative tem¬ 
perature of bodies, and some other method must be re¬ 
sorted to for reliable measurement. The one most ex¬ 
tensively used is based on the regular increase in the vol¬ 
ume of a body attending a rise in its temperature. This 
method is illustrated by the common mercurial ther¬ 
mometer. 


282 


HEAT 


II. THE THERMOMETER 

323. The Thermometer. — The common mercurial ther¬ 
mometer consists of a capillary glass tube of uniform bore, 
on one end of which is blown a bulb, either 
spherical or cylindrical (Fig. 301). Part of 
the air is expelled by heating, and while in 
this condition the open end of the tube is 
dipped into a vessel of pure mercury. As 
the tube cools, mercury is forced into the 
tube by atmospheric pressure. Enough mer¬ 
cury is introduced to fill the bulb and part 
of the tube at the lowest temperature which 
the thermometer is designed to measure. 
Heat is now applied to the bulb until the ex¬ 
panded mercury fills the tube; the end is 
then closed in the blowpipe flame. The 
mercury contracts as it cools, leaving the 
larger portion of the capillary empty. 

324. The Necessity of Fixed Points.—No 
two thermometers are likely to have bulbs 
and stems of the same capacity. Conse¬ 
quently, the same increase of temperature 
will not produce equal changes in the length of the thread 
of mercury. If, then, the same scale were attached to all 
thermometers, their indications would differ so widely 
that the results would be worthless. Hence, if ther¬ 
mometers are to be compared, corresponding divisions on 
the scale of different instruments must indicate the same 
temperature. This may be done by graduating every 
thermometer by comparison with a standard, an expensive 
proceeding and for many purposes unnecessary, since mer¬ 
cury has a nearly uniform rate of expansion. If two 


C F 

a ft 


Figure 301. 
— C. and F. 
Thermome¬ 
ters. 











MARKING THE FIXED POINTS 


283 



points are marked on the stem, the others can be obtained 
by dividing the space between them into the proper num¬ 
ber of equal parts. Investigations have made it 
certain that under a constant pressure the tem¬ 
perature of melting ice and that of steam are in¬ 
variable. Hence, the temperature of melting ice 
and that of steam under a pressure of 76 cm. of 
mercury (one atmosphere) have been chosen as 
the fixed points on a thermometer. 

325. Marking the Fixed Points.—The ther¬ 
mometer is. packed in finely broken ice, as far up 
the stem as the mercury extends. The contain¬ 
ing vessel (Fig. 302) has an opening at the bot¬ 
tom to let the water run out. After standing in _ 

the ice for several minutes the Figure 
top of the thread of mercury is 2 0 2 • ~ 
marked on the stem. This is p 0INT> 
called the freezing point. 

The boiling point is marked by observ¬ 
ing the top of the mercurial column when 
the bulb and stem are enveloped in steam 
(Fig. 303) under an atmospheric pressure 
of 76 cm. (29.92 in.). If the pressure at 
the time is not 76 cm., then a correction 
must be applied, the amount being de¬ 
termined by the approximate rule that 
the temperature of steam rises 0.1° C. 
for every increase of 2.71 mm. in the 
barometric reading, near 100° C. 

326. Thermometer Scales. — The dis¬ 
tance between the fixed points is divided 
into equal parts called degrees. The number of such parts 
is wholly arbitrary, and several different scales have been 



Figure 303.— 
Marking the Boil¬ 
ing Point. 















284 


HEAT 


introduced. The number of thermometer scales in use in 
the eighteenth century was at least nineteen. Fortunately 
all but three of them have passed into ancient history. 

The Fahrenheit scale, which is in general use in English- 
speaking countries, appears to have made its first appear¬ 
ance about 1714, but the earliest published description of 
it was in 1724. At that time this scale b.egan af^0° and 
ended at 96°. Fahrenheit describes his scale as deter¬ 
mined by'tRree points: the lowest wasJdjejO 0 and was 
found by a mixture of ice, water, and sea salt; the next 
was the 82° point and was found by dipping the ther¬ 
mometer into a mixture of ice and water without salt; 
the third was marked 96°, the point to which alcohol 
expanded “ if the thermometer be held in the mouth or 
armpit of a healthy person.” When this scale was ex¬ 
tended, the boiling point was found to be 212°. The 
space between the freezing and the boiling point is there¬ 
fore 180°. 

The Centigrade scale was introduced by Celsius, pro¬ 
fessor of astronomy in the University of Upsala, about 
1742. It differs from the Fahrenheit in making the freez¬ 
ing point fl\and the boiling point 100°, the space between 
being divided into 100 equal parts or degrees. The sim¬ 
plicity of Celsius’s division of the scale has led to its 
general adoption in all countries for scientific purposes, 
and in many for domestic and industrial use. 

The scale in both thermometers is extended beyond the 
fixed points as far as desired. The divisions below 0° 
are read as minus and are marked with the negative sign. 
The initial letters F. and C. denote the Fahrenheit and 
Centigrade scales respectively. 

327. The Two Scales Compared. — In Fig. 804 AB is 
a thermometer with two scales attached, P is the head 


THE CLINICAL THERMOMETER 


285 


of the mercury column, and F and <7 are the readings 
on the scales respectively. On the Fahrenheit scale, 
A£ = 180 and AP 


= F — 32, since the 
zero is 32 spaces be¬ 
low A; on the Centi¬ 
grade, AB — 100 and 
AP = (7. Then the ratio of AP to AB is 


A 

P 

B 




Fahrenheit 3|2 

F 

2 

12 

Centigrade |q 

C 

1 

00 


Figure 304. — Scales Compared. 

F- 32 = C 
180 100 


By substituting the reading on either scale in this equa¬ 
tion the equivalent on the other scale is easily obtained. 
For example, if it is required to express 68° F. on the 

68 -32 O 


Centigrade 


scale, then 


180 


100 ’ 


whence 


(7= 20°. 

328. Limitations of the Mercurial Thermometer. — 

As mercury freezes at — 38.8° C., it cannot be 
used as the thermometric substance below this 
temperature. For temperatures below — 38° C. 
alcohol is substituted for mercury. Under a pres¬ 
sure of one atmosphere mercury boils at about 
350° C. For temperatures approaching this value 
and up to about 550° C. the thermometer stem is 
filled with pure nitrogen under pressure. The 
pressure of the gas keeps the mercury from boiling 
(§ 356). 

329. The Clinical Thermometer. — The clinical 
thermometer is a sensitive instrument of short 
range for indicating the temperature of the human 
body. It is usually graduated from 95° to 110° 

Figure F., or from 85 ° to 45 ° There is a constriction 
305. — in the tube just above the bulb (Fig. 305), which 
T L hTr L causes the tliread of mercury to break at that point 
mometer. when the temperature begins to fall, leaving the 



















286 


HEAT 


top of the separated thread to mark the highest tempera¬ 
ture registered. A sudden jerk or tapping of the ther¬ 
mometer forces the mercury down past the constriction 
and sets it for a new reading. The normal temperature 
of the human body is 98.6° F. or 37° C. 

Questions and Problems 

1. Why do the degree spaces differ in length on different ther¬ 
mometers of the same scale ? 

2 . What advantages does a thermometer with a cylindrical bulb 
have over one with a spherical bulb ? 

3. Why is mercury preferable to other liquids for use in ther¬ 
mometers ? 

4. Why is it necessary to have fixed points in thermometers? 

5. The bulb of a thermometer generally contracts a little after 
the thermometer is completed. What is the result on the readings? 

6. Why is nitrogen used in preference to oxygen in thermometers 

for high temperatures ? • 

7. Why should the thermometer tube be of uniform bore? 

8 . Express in Fahrenheit degrees the following 4° C., 30° C., 
- 38° C. 

9. Express in Centigrade degrees the following 39° F., — 40° F., 
68° F. 

10 . The fixed points on a Centigrade thermometer were found to 
be incorrect; the freezing point read 2° and the boiling point 99°. 
When this thermometer was immersed in a liquid the reading was 
50°. What was the correct temperature of the liquid ? 

(Note. — Compare this incorrect thermometer with a correct one 
just as a Fahrenheit thermometer is compared with a Centigrade in 
§ 327.) 

11 . A thermometer read 40° C. in a water bath. When tested it 
was found to read 0° at the freezing point, but 95° instead of 100° at 
the boiling point. What was the correct temperature of the bath ? 

12. If a Fahrenheit thermometer read- 210° in steam and 31° in 
melting ice, what would it read as the equivalent of 70° F. ? 


EXPANSION OF SOLIDS 


287 


13. A correct Fahrenheit thermometer read 70° as the temperature 
of a room. An incorrect Centigrade thermometer read 20° in the 
same room. What was the error of the latter? 

14. A certain Centigrade thermometer reads 2° in melting ice and 
100° in steam under normal atmospheric pressure. What is the 
correct value for a reading of 25° on this thermometer ? 


III. EXPANSION 

330. Expansion of Solids. —Insert a long knitting needle A 
in a block of wood so as to stand vertically (Fig. 306). A second 
needle D is supported paral¬ 
lel to the first by means of a 
piece of cork or wood C. 

The lower end of D just 
touches the mercury in the 
cup H. An electric circuit 
is made through the mer¬ 
cury, the needle, an electric 
battery, and the bell B, as 
shown. Now apply a Bun¬ 
sen flame to A ; D will be 
lifted out of the mercury and 
the bell will stop ringing. 

Then heat D or cool A , and 
the contact of D with the mer¬ 
cury will be renewed as shown 
by the ringing of the bell. 

This experiment shows that solids expand in length 
when heated and contract when cooled. To this rule of 
expansion there are a few exceptions, notably iodide of sil¬ 
ver and stretched india-rubber. 

Rivet together at short intervals a strip of sheet copper and one of 
sheet iron D (Fig. 307). Support this compound bar so as to play 
between two points A and C, which are connected through the battery 
P and the bell B. Apply a Bunsen flame to the bar. It will warp, 









288 


HEAT 



Figure 307. — Unequal Expansion. 

The experiment shows that the two metals expand 
unequally and cause the bar to warp. 



Figure 308.— Expansion of 
Ball. 


Figure 308 illustrates a piece of ap¬ 
paratus known as Gravesande’s ring. 
It consists of a metallic ball that at 
ordinary temperatures will just pass 
through the ring. Heat the ball in 
boiling water. It will now rest on the 
ring and will not fall through until it 
has cooled. 

We conclude that the ex¬ 
pansion of a solid takes place 
in every direction. 


331. Expansion of Liquids. — Select two 
four-inch test tubes, fit to each a perforated 
stopper, through which passes a small glass tube 
about six inches long. The capacity of the two 
test tubes after stoppers are inserted should be 
equal. Fill one tube with mercury and the other 
with glycerine colored with an aniline dye. Set 
the test tubes in a beaker of water over a Bunsen 
flame (Fig. 309) and note the change in the 
height of the liquids in the tubes. 

Two facts are illustrated: first, liquids 
are affected by heat in the same way as 



Figure 309. —Ex¬ 
pansion of Liquids. 




















COEFFICIENT OF LINEAR EXPANSION 


289 


solids ; second, the expansion of the liquids is greater than 
that of the glass or there would be no apparent increase in 
their volume. 

Some liquids do not expand when heated at certain 
points on the thermometric scale. Water, for example, 
on heating from 0° C. to 4° C. contracts, but above 4° C. 
it expands. 

332. Expansion of Gases. — Fit a bent delivery tube to a small 
Florence flask (Fig. 310). Fill the flask with air and place the up¬ 
turned end of a delivery tube under an inverted graduated glass 
cylinder filled with water. Heat 
the flask by immersing it in a 
vessel of moderately hot water. 

The air will expand and escape 
through the delivery tube into 
the cylinder; note the amount. 

Now refill the flask with some 
other gas, as coal gas, and re¬ 
peat the experiment. The amount 
of gas collected will be nearly the 
same. Figure 310. — Expansion of Gases. 

Investigation has shown that all gases which are hard to 
liquefy expand very nearly alike at atmospheric pressure, 
approaching equality as the pressure is diminished. Gases 
that are easily liquefied, as carbon dioxide, show the largest 
variation in the expansion. 

333. Coefficient of Linear Expansion.—Nearly all solids 
expand with increase of temperature, but they do not 
expand equally. Assume three rods of the same length, — 
zinc, brass, and steel. With the same rise of temperature, 
the zinc rod will increase in length 50 per cent more than 
the brass, and the brass nearly 50 per cent more than the 
steel. A brass bar will expand in length 20 times as 
much as a bar of “ invar ” (nickel steel) if the bars are 









290 


HEAT 


of the same length and undergo the same change of 
temperature. 

The coefficient of linear expansion, or expansion in length, 
expresses this property of expansion in a numerical way. 
It is the increase in a unit length of a substance per degree 
increase in temperature. This is equivalent to the ex¬ 
pression : 

Coefficient of linear expansion 

_ increase in length _ 

original length x temp, change 


If l x and l 2 denote the lengths of a metallic rod at tem¬ 
peratures ti and t 2 respectively, then ^—— 1 = ^^ is the 

t 2 11 t 

whole expansion for 1°; t is the difference of temperature. 

If a denotes the coefficient of expansion, then a 
whence Z 2 = Z x (l 4- at'). 

Since this coefficient is a ratio, it makes no difference 
what unit of length is used. Coefficients of expansion are 
usually given in terms of the Centigrade degree. For 
the Fahrenheit degree the coefficient is, of course, ^ as 
great as for the Centigrade. 




Some Coefficients of Linear Expansion 


Invar. 0.0000009 Copper ..... 0.0000172 

Glass. 0.0000086 Brass. 0.0000188 

Platinum .... 0.0000088 Silver. 0.0000191 

Cast Iron .... 0.0000113 Tin. 0.0000217 

Steel. 0.0000132 Zinc. 0.0000294 


334. Illustrations of Linear Expansion. — Many familiar facts 
are accounted for by expansion or contraction attending changes of 
temperature. If hot water is poured into a thick glass tumbler, the 
glass will probably crack by reason of the stress produced by the 









































































































Bridge over the Firth of Forth. 

Allowance for the expansion and contraction of the steel must be made 

in the construction. 








COMPENSATED CLOCKS AND WATCHES 291 


sudden expansion of its inner surface. On the other hand, crucibles 
and other laboratory utensils are now made of clear fused quartz; fused 
quartz has so small a coefficient of expansion that a red-hot crucible 
may be plunged into water without cracking. The coefficients of 
glass and platinum are so nearly equal that platinum wires may be 
sealed into glass without cracking the latter when it cools. 

Crystalline rocks, on account of unequal expansion in different 
directions, are slowly disintegrated by changes of temperature; and 
for the same reason quartz crystals, when strongly heated, fly in 
pieces. The outcropping granite hills of the celebrated South African 
Matopos have been broken into huge boulders and irregular masses 
by the large expansion in the fervid heat of midday and the subse¬ 
quent rapid contraction during the low temperature of the succeeding 
night. 

In long steel bridges built in cold climates considerable expansion 
occurs in summer, and a certain freedom of motion of the parts must 
be provided for. Long suspension bridges are several 
inches higher at the middle in midwinter than in the heat 
of summer. Long steam pipes are fitted with expansion 
joints to permit one part to slide into the other; bends or 
elbows in the pipe are also used, so that the pipe may ac¬ 
commodate itself to the expansion. 

335. Compensated Clocks and Watches. — If the 
length of a pendulum changes with temperature, the period 
of vibration will also change and the clock will not have a 
constant rate. The balance wheel of a watch serves a 
similar purpose of regulating the period of vibration and 
is similarly affected by changes in temperature. To com¬ 
pensate foi; these changes so as to keep the period of vi¬ 
bration constant, the principle of unequal expansion is em¬ 
ployed. 

The bob of a compensated mercurial pendulum consists 
of one or more glass jars, nearly filled with mercury, and Figure 
attached to the lower end of a steel rod (Fig. 311). A 311 . — 
rise of temperature lengthens the rod and lowers the Mercu- 
center of oscillation; but the mercury expands upward rialPen- 
and compensates by raising the center of oscillation. By DULUM * 
a proper adjustment of the quantity of mercury in the tubes, its 
expansion may be made to compensate for that of the rod. 












292 


HEAT 


The rate of a watch depends largely on the balance wheel. Unless 
this is compensated, it expands when the temperature rises and the 
watch loses time, the larger wheel oscillating 
more slowly under the force supplied by the 
elasticity of the hairspring. Compensation is 
secured by making the rim of the wheel in two 
sections, each being made of two materials and 
supported by one end on a separate arm (Fig. 
312). The more expansible metal is on the out¬ 
side. When the temperature rises and the radial 

Figure 312.— Com- arms expand, the loaded free ends a, a f of the 
Wheel TED ^ ALANCE sections move inward, thus compensating for the 
increased length of the radial arms. The final 
adjustment is made by screwing in or out the studs on the rim. 

336. Cubical Expansion. — In general, solids and liquids 
when heated expand in all directions with increase of 
volume. This expansion in volume is called cubical ex¬ 
pansion. The coefficient of cubical expansion is the increase 
in volume of a unit volume per degree rise of temperature. 

Precisely as in the case of linear expansion, the coeffi¬ 
cient of cubical expansion 7c may be expressed by the 
eq uation 

k = ^zh. 

Vf, 

Whence v 2 = v 1 (l -f let). 

The coefficient of cubical expansion of a substance is 
three times its coefficient of linear expansion. Thus if 
the coefficient of linear expansion of cast iron is 0.0000113, 
its coefficient of cubical expansion is 0.0000339. 

337. Expansion of Water. —Water exhibits the remark¬ 
able property of contracting when heated at the freezing 
point. This contraction continues up to 4° C., when ex¬ 
pansion sets in. The greatest density of water is therefore 
at 4° C., and its density at 6° is nearly the same as at 2°. 




THE ABSOLUTE SCALE 


293 


In a lake or pond water at 4° sinks to the bottom, while 
water below 4° is lighter and rises to the top, where the 
freezing begins. Ice forms at the surface of a body of 
cold water, which freezes from the surface downwards. 
Fishes are thus protected from freezing. 

338. Law of Charles.—It was shown by Charles, in 
178T, that the volume of a given mass of any gas under 
constant pressure increases by a constant fraction of its 
volume at zero for each rise of temperature of 1 ° C. The 
investigations of Regnault and others show that the law 
is not rigorously true, and that the accuracy of Charles’s 
law is about the same as that of Boyle’s law. The coeffi¬ 
cient of expansion k of dry air is 0.003665, or about ^ 3 . 
This fraction may be considered as the coefficient of ex¬ 
pansion of any true gas. 

339. The Absolute Scale. — The law of Charles leads to 
a scale of temperature called the absolute scale. By this 
law the volumes of any mass of gas, under constant pres¬ 
sure, at 0° C., and at any other temperature t° C., are 
connected by the following relations (§ 336) : 

v = v 0 (\ + ^t' ) = v A^±Tl .. . . (a) 


At any other temperature, *\ the volume becomes 


, _ fl 0 (273 + *') 

273 

Divide ( a ) by (5) and 

v 273 + * 

v' 273 + *'* 


(A) 


Suppose now a new scale is taken, whose zero is 273 
Centigrade divisions below the freezing point of water, 





294 


HEAT 


and that temperatures on this scale are denoted by T. 
Then 273 +£ will be represented by T, and 273+ £' by 
T\ and 


273-M 
273 + 1' 


T 

yr/’ 


or the volumes of the same mass of gas under constant pres¬ 
sure are proportional to the temperatures on this new scale. 
The point 273° below 0° C. is called the absolute zero , and 
the temperatures on this scale, absolute temperatures. Up 
to the present it has not been found possible to cool a 
body to the absolute zero; but by evaporating liquid 
hydrogen under very low pressure, a temperature esti¬ 
mated to be within 9° of the absolute zero has been ob¬ 
tained by Professor Dewar; and Professor Onnes, by 
liquefying helium, believes that he obtained a tempera¬ 
ture within 2° or 3° of the absolute zero. 

At these low temperatures steel and rubber become as 
brittle as glass. 

340. The Gas Equation. — The laws of Boyle and Charles 
may be combined into one expression, which is known as 
the gas equation. It has a wider application even than its 
method of derivation would indicate. 

Let v 0 , p 0 , T q be the volume, pressure, and absolute tem¬ 
perature of a given mass of gas. 

Also let v, p, T be the corresponding quantities for the 
same mass of gas at pressure p and temperature T. 

Then applying Boyle’s law (§ 87) to increase the pres¬ 
sure to the value the temperature remaining constant, 
we have 

v ' Pa 


where v f is the new volume corresponding to the pres¬ 
sure p. 




QUESTIONS AND PROBLEMS 


295 


Next apply the law of Charles (§ 339), keeping the 
pressure constant at the value jt?, and starting with the 
new volume v' . Then since the volumes are directly 
proportional to the temperatures, we have 



where v is the new volume corresponding to temperature T. 
Multiply (a) and (6) together member by member, and 

-o = or -2^0 = ^ = a constant, since p and T are any 

* Pj T o T F y 

pressure and temperature and v corresponds. This con¬ 
stant is usually denoted by R. We may therefore write 

pv = RT. . . . (Equation 33) 


To illustrate the use of the above relation : If 20 cm. 8 of gas at 
20° C. is under a pressure of 76 cm. of mercury, what will be the 
pressure when its volume is 30 cm. 8 and temperature 50° C.? 


From equation (33), is a constant, 


or 


pv _ p'v' 
T~ T' ’ 


Hence 
from which 


76 x 20 _ p x 30 
273 + 20 “ 273 + 50’ 

p — 55.85 cm. 


Questions and Problems 

1. Telegraph wires often “ hum ” in the wind. Why is the pitch 
higher in winter than in summer ? 

2. When a piece of ice floats, about ^ of its volume projects out 
of the water. If a pan is level full of water and a piece of ice floats 
in it, both at 0° C., why is there no change of level when the ice 
melts? 

3. Why is a fountain pen more likely to leak when nearly empty ? 




296 


HEAT 


4 . If the bulb of a mercurial thermometer is plunged into hot- 
water, the top of the thread of mercury first falls and then rises. 
Explain. 

5 . A copper rod 125 cm. long at 0° C. expands to 125.209 cm. at 
100° C. Find the coefficient of linear expansion of copper. 

6. The coefficient of linear expansion of steel is 0.0000132. What 
will be the variation in length of a steel bridge 250 ft. long between 
the temperatures — 10° C. and 40° C.? 

7 . The coefficient of linear expansion of steel is 0.0000132 and 
that of zinc is 0.0000294. What relative lengths of rods of these 
metals will have equal expansions in length for the same changes of 
temperature ? 

8. The coefficient of the volume expansion of glass is 0.000258. 
A density bottle at 15° C. holds 25 cm. 3 . What will be its capacity 
at 25° C.? 

9 . Why should the reading of the mercurial barometer be cor¬ 
rected for temperature ? If the relative volume coefficient of expan¬ 
sion of mercury in glass is 0.000155, and the barometer reads 755 mm. 
at 20° C., what would be the reduced reading at 0° C.? 

10. The volume of a given mass of gas at 740 mm. pressure is 
1200 cm. 3 ; find its volume at 760 mm. 

11. The mass of a liter of air at 0° C. and 76 cm. pressure is 1.3 g. 
Find the mass of 10 liters of air at 20° C. and 74 cm. pressure. 

12. A liter of hydrogen at 15° C. is heated at constant pressure to 
75° C. Find its volume. 

13 . A quantity of gas is collected in a graduated tube over mer¬ 
cury. The reading of the mercury level in the tube is 20 cm., the 
volume of the gas is 60 cm. 3 , the temperature is 20° C., and the ba¬ 
rometer reading is 74 cm. How many cubic centimeters of gas are 
there at 0° C. and 76 cm. pressure? 

14 . Three cubic centimeters of air are introduced into the vacuum 
of a mercurial barometer. The barometer read 76 cm. before intro¬ 
ducing the air and 57 cm. after. What volume does the air occupy in 
the barometer ? 


SPECIFIC HEAT 


297 


IV. MEASUREMENT OF HEAT 

341. The Unit of Heat. —The unit of heat in the c. g. s. 
system is the calorie. It is defined as the quantity of heat 
that will raise the temperature of one gram cf water one de¬ 
gree Centigrade. There is no agreement as to the position 
of the one degree on the thermometric scale, although it is 
known that the unit quantity of heat varies slightly at 
different points on the scale. If the degree interval 
chosen is from 15° to 16° C., the calorie is then the one 
hundredth part of the heat required to raise the tempera¬ 
ture of one gram of water from 0° to 100° C. 

In engineering practice in England and America the 
British thermal unit (B. T. U.) is commonly employed. It 
is the heat required to raise the temperature of one pound 
of water one degree Fahrenheit. 

342. Thermal Capacity. — The thermal capacity of a body 
is the number of calories required to raise its temperature 
one degree Centigrade. The thermal capacity of equal 
masses of different substances differs widely. For example, 
if 100 g. of water at 0° C. be mixed with 100 g. at 100° C., 
the temperature of the whole will be very nearly 50° C. 
But if 100 g. of copper at 100° C. be cooled in 100 g. of 
water at 0° C., the final temperature will be about 9.1° C. 
The heat lost by the copper in cooling through 90.9° is 
sufficient to heat the same mass of water only 9.1°, that is, 
the thermal capacity of water is about ten times as great 
as that of an equal mass of copper. 

343. Specific Heat. — The specific heat of a substance is 
the number of calories of heat required to raise the tem¬ 
perature of one gram of it through one degree Centigrade. 
It may be defined independently of any temperature scale 
as the ratio between the number of units of heat required 


298 


HEAT 


to raise the temperature of equal masses of the substance 
and of water through one degree. The specific heat of 
mercury is 0.033, that is, the heat that will raise 1 g. of 
mercury through 1° C. will raise 1 g. of water through 
only 0.033° C. 

The specific heat of water is twice as great as that of ice 
(0.505), and more than twice as great as that of steam 
under constant pressure (0.4TT). 

344. Numerical Problem in Specific Heat. — The principle ap¬ 
plied in the solution of such problems is that the gain or loss of heat 
by the water is equal to the loss or gain of heat by the body introduced 
into the water. The gain or loss of heat by the body is equal to the 
product of its mass, its specific heat, and its change of temperature. 

To illustrate: 20 g. of iron at 98° C. are placed in 75 g. of water at 
10° C. contained in a copper beaker weighing 15 g., specific heat 0.095. 
The resulting temperature of the water and the iron is 12.5° C. Find 
the specific heat of iron. \ 

The thermal capacity of the beaker is 15 x 0.095 = 1.425 calories. 
The heat lost by the iron is 20 x s x (98 — 12.5) calories, in which s 
represents the specific heat of iron, and (98 — 12.5) its change of tem¬ 
perature. The heat gained by the water and the copper vessel is (75 4- 
1.425) x (12.5 — 10) calories ; the second factor is the gain in temper¬ 
ature of the water and the beaker. It follows by equating these two 
quantities that 20 x s x (98 — 12.5) = (75 + 1.425) x (12.5 — 10). 
Solving for s, we have s = 0.112 calorie per gram. 

Questions and Problems 

1. What is the specific heat of water ? 

2. A pound of water and a pound of lead are subjected to the 
same source of heat for 10 min. Which will be at the higher tem¬ 
perature ? 

3 . If equal quantities of heat are applied to equal masses of iron 
and lead, which will show the greater change of temperature ? 

4 . Equal balls of iron and zinc are heated in boiling water and 
are placed on a cake of beeswax. Which will melt the further into 
the wax ? 


THE MELTING POINT 


299 


5 . Why is water better than any other liquid for heating purposes ? 

6. Why is a rubber bag filled with hot water better for a foot 
warmer than an equal mass of any solid ? 

7. A copper beaker has a mass of 25 g. The specific heat of cop¬ 
per is 0.095. What is the thermal capacity of the beaker? 

8. How much heat will it take to raise a liter of water from 20° C. 
to 100° C.? 

9 . The specific heat of iron is 0.112. How much heat will be re¬ 
quired to raise 250 g. of iron from 10° to 45° C. ? 

10 . 120 g. of water at 5° C. are mixed "with 200 g. of water at 50° C. 
Assuming that no heat is lost, what will be the resulting temperature ? 

11 . 89.2 g. of iron at 90° C. are placed in 70 g. of water at 10° C.; 
the resulting temperature is 20° C. Find the specific heat of iron. 

12 . A copper ball weighing 1 kg. has a specific heat of 0.095. It 
is heated in a furnace to the temperature of the furnace and dropped 
into a liter of water at 10° C. The temperature of the water rises to 
93.1° C. Find the temperature of the furnace. 

13 . How many calories in the British Thermal Unit ? 

14 . A glass beaker weighs 100 g. If the specific heat of the glass 
is 0.177, how much water will have the same thermal capacity as the 
beaker? 

15 . Why do islands in the sea have smaller extremes of temperature 
than inland areas ? 

V. CHANGE OF STATE 

345. The Melting Point. — A body is said to melt or fuse 
when it changes from the solid to the liquid state by the 
application of heat. The change is called melting, fusion, 
or liquefaction. The temperature at which fusion takes 
place is called the melting point. Solidification or freezing 
is the converse of fusion, and the temperature of solidifi¬ 
cation is usually the same as the melting point of the 
same substance. Water, if undisturbed, may be cooled a 
number of degrees below 0° C., but if it is disturbed it 


800 


HEAT 


usually freezes at once, and its temperature rises to the 
freezing point. 

The melting point of crystalline bodies is well marked. 
A mixture of ice and water in any relative proportion 
will remain without change if the temperature of the room 
is 0° C.; but if the temperature is above zero, some of the 
ice will melt; if it is below zero, some of the water will 
freeze. Some substances, like wax, glass, and wrought 
iron, have no sharply defined melting point. They first 
soften and then pass more or less slowly into the condition 
of a viscous liquid. It is this property which permits of 
the bending and molding of glass, and the rolling, welding, 
and forging of iron. 

346. Change in Volume accompanying Fusion. — Fit to a 

small bottle a perforated stopper through which passes a fine glass 
tube. Fill with w T ater recently boiled to expel the air, the water ex¬ 
tending halfway up the tube. Pack the apparatus in a mixture of 
salt and finely broken ice. The water column at first will fall slowly, 
but in a few minutes it will begin to rise, and will continue to do so 
until water flows out of the top of the tube. The water in the bottle 
freezes, expands, and causes the overflow. 

Most substances occupy a larger volume in the liquid 
state than in the solid; that is, they expand in liquefying. 
A few substances, like water and bismuth, expand in 
solidifying. When water freezes, its volume increases 
9 per cent. If this expansion is resisted, water in freezing 
is capable of exerting a force of about 2000 kg. per 
square centimeter. This explains the bursting of water 
pipes when the water in them freezes, and the rending of 
rocks by the freezing of water in cracks and crevices. The 
expansion of cast iron and type metal when they solidify 
accounts for the exact reproduction of the mold in which 
they are cast. 


BEAT OF FUSION 


301 


347. Effect of Pressure on the Melting Point. — Support a 
rectangular block or prism of ice on a stout bar of wood. Pass a 
thin iron wire around the ice and the bar of wood, and suspend on it 
a weight of 25 to 50 lb. The pressure of the wire lowers the melting 
point of the ice immediately under it and the ice melts ; the water, 
after passing around the wire, where it is relieved of pressure, again 
freezes. In this way the wire passes slowly through the ice, leaving 
the block solidly frozen. 

A rough numerical statement of the effect of pressure 
on the freezing point of water is that a pressure of one 
ton per square inch lowers the freezing point to — 1° C. 
Familiar examples of refreezing, or regelation , are the 
hardening of snowballs 
under the pressure of 
the hands, the formation 
of solid ice in a roadway 
where it is compressed 
by vehicles and the hoofs 
of horses, and frozen 
footforms in compact ice 
after the loose snow has 
melted around them. 

The ice of a glacier melts 
where it is under the 
enormous pressure of 
the descending masses HiourE 3 1 3._ MerdeGlace , Chamoun , x . 
above it. The melting 

permits the ice to accommodate itself to abrupt changes 
in the rocky channel, and a slow iceflow results. As soon 
as the pressure at any surface is relieved, the water again 
freezes (Fig. 313). 

348. Heat of Fusion. — When a solid melts, a quantity 
of heat disappears; and, conversely, when a liquid solidi¬ 
fies, the amount of heat generated is the same as dis- 





302 


HEAT 


appears during liquefaction. The heat of fusion of a 
substance is the number of calories required to melt a 
gram of it without change of temperature. The heat of 
fusion of ice is 80 calories. 

As an illustration of the heat of fusion, place 200 g. of clean ice, 
broken into small pieces, into 500 g. of water at 60° C. When the 
ice has melted, the temperature will be about 20° C. The heat lost 
by the 500 g. of water equals 500 x (60 — 20) = 20,000 calories. This 
heat goes to melt the ice and to raise the resulting water from 0° C. to 
20° C. To raise this water from 0° to 20° requires 200 x 20=4000 
calories. The remainder, 20,000 — 4000 = 16,000 calories, went to 
melt the ice. Then the heat of fusion of ice is 16,000 200 = 80 

calories per gram. 

349. Heat lost in Solution. — Fill a beaker partly full of water 
at the temperature of the room, and add some ammonium nitrate 
crystals. The temperature of the water will fall as the crystals dissolve. 

This experiment illustrates the fact that heat disap¬ 
pears when a body passes from the solid to the liquid 
state by solution. The use of salt in soup or of sugar 
in tea absorbs heat. The heat energy is used to pull 
down the solid structure. 

350. Freezing Mixtures. — Freezing mixtures are based 
on the absorption of heat necessary to give fluidity. Salt 
water freezes at a lower temperature than fresh water. 
When salt and snow or pounded ice are mixed together, 
both become fluid and absorb heat in the passage from 
the one state to the other. By this mixture a tempera¬ 
ture of — 22° C. may be obtained. Still lower tempera¬ 
tures may be reached with other mixtures, notably with 
sulpho-cyanide of sodium and water. 

351. Vaporization. — Pour a few drops of ether into a beaker 
and cover closely with a plate of glass. After a few seconds bring 
a lighted taper to the mouth of the beaker. A sudden flash will 
show that the vapor of ether was mixed with the air. 


COLB BY EVAPORATION 


303 


Support on an iron stand a Florence flask two-thirds full of water 
and apply heat. In a short time bubbles of steam will form at the 
bottom of the flask, rise through the water, and burst at the top, pro¬ 
ducing violent agitation throughout the mass. 

Vaporization is the conversion of a substance into the 
gaseous form. If the change takes place slowly from 
the surface of a liquid, it is called evaporation ; but if the 
liquid is visibly agitated by rapid internal evaporation, 
the process is called ebullition or boiling. 

352. Sublimation. — When a substance passes directly 
from the solid to the gaseous form without passing 
through the intermediate state of a liquid, it is said to 
sublime. Arsenic, camphor, and iodine sublime at atmos¬ 
pheric pressure, but if the pressure be sufficiently in¬ 
creased, they may be fused. Ice also evaporates slowly 
even at a temperature below freezing. Frozen clothes 
dry in the air in freezing weather. At a pressure less 
than 4.6 mm. of mercury, ice is converted into vapor by 
heat without melting. 

353. The Spheroidal State. — When a small quantity of 
liquid is placed on hot metal, as water on a red-hot stove, 
it assumes a globular or spheroidal form, and evaporates 
at a rate between ordinary evaporation and boiling. It 
is then in the spheroidal state. The vapor acts like a 
cushion and prevents actual contact between the liquid 
and the metal. The globular form is due to surface ten¬ 
sion. Liquid oxygen at — 180° C. assumes the spheroidal 
form on water. The temperature of the water is rela¬ 
tively high compared with that of the liquid oxygen. 

354. Cold by Evaporation. — Tie a piece of fine linen around the 
bulb of a thermometer and pour on it a few drops of sulphuric ether. 
The temperature will at once begin to fall, showing that the bulb 
has been cooled. 


304 


HEAT 


In tlie evaporation of.ether, some of the heat of the 
thermometer is used to do work on the liquid. 

Sprinkling the floor of a room cools the air, because of 
the heat expended in evaporating the water. Porous 
water vessels keep the water cool by the evaporation of 
the water from the outside surface. Liquid carbon 
dioxide is readily frozen by its own rapid evaporation. 
Dewar liquefied oxygen by means of the temperature 
obtained through the successive evaporation of liquid 
nitrous oxide and ethylene. Similarly, by the evapora¬ 
tion of liquid air he has liquefied hydrogen. The evapo¬ 
ration of liquid hydrogen under reduced pressure has 



enabled him to obtain a temperature but little removed 
from the absolute zero, — 273° C. More recently Pro¬ 
fessor Onnes of Leyden, by the evaporation of liquid 
helium, has reached the extremely low temperature of 
— 271.3° C. or 1.7° absolute. 

355. Ammonia Ice Plant. — The low temperature produced by 
the rapid evaporation of liquid ammonia is utilized in the manufac¬ 
ture of ice and for general cooling in refrigerator plants. Ammonia 
may be liquefied by pressure alone. At a temperature of 80° F. the 








































EFFECT OF PRESSURE OX THE BOILING POINT 305 


required pressure is 155 pounds per square inch. The essential parts 
of an ice plant are shown in Fig. 314. Gaseous ammonia is com¬ 
pressed by a pump in condenser pipes, over which flows cold water to 
remove the heat. From the condenser the liquid ammonia passes 
very slowly through a regulating valve into the pipes of the evapo¬ 
rator. The pressure in the evaporator is kept low by the pump, which 
acts as an exhaust pump on one side and as a compressor on the other. 
The pump removes the evaporated ammonia rapidly and the evapora¬ 
tion absorbs heat. The pipes in which the evaporation takes place 
are either in a tank of brine, or in the refrigerating room. Smaller 
tanks of distilled water are placed in the brine until the water in 
them is frozen. The pipes in the refrigerating room are covered with 
hoar frost, which is frozen moisture from the air. The temperature of 
the brine is reduced to about 16° to 18° F. 

The brine does not freeze at this tempera¬ 
ture. 

The process is continuous because the 
gaseous ammonia is returned to the con¬ 
densing coils, which are cooled with water. 

It thus passes repeatedly through the same 
cycle of physical changes. 

356. Effect of Pressure on the Boil¬ 
ing Point. — Place a flask of warm water 
under the receiver of an air pump. It 
will boil violently when the receiver is ex¬ 
hausted. 

Fill a round-bottomed Florence flask 
half full of water and heat until it boils 
vigorously. Cork the flask, invert, and sup¬ 
port it on a ring stand (Fig. 315).. The boiling ceases, but is re¬ 
newed by applying cold water to the flask. The cold water condenses 
the vapor, and reduces the pressure within the flask so that the boil¬ 
ing begins again. 

The effect of pressure on the boiling point is seen in 
the low temperature of boiling water at high elevations, 
and in the high temperature of the water under pressure 
in digesters used for extracting gelatine from bones. The 
boiling point of water falls 1° C. for an increase in eleva- 



Figure 315. — Boiling 
under Reduced Pressure. 
















306 


HEAT 


tion of about 295 in. At Quito the boiling point is near 


90° C. 


357. Heat of Vaporization. — The heat of vaporization is 
the number of calories required to change one gram of a 
liquid at its boiling point into vapor at the same tempera¬ 
ture. Water has the greatest heat of vaporization of all 
liquids. The most carefully conducted experiments show 
that the heat of vaporization of water under a pressure of 


one atmosphere is 536.6 calo¬ 
ries per gram. 



Set up apparatus like that shown 
in Fig. 316. The steam from the 
boiling water is conveyed into a 
beaker containing a known quantity 
of water at a known temperature. 
The increase in the mass of water 
gives the amount of steam con¬ 
densed. The “ trap ” in the delivery 
tube catches the water that condenses 
before it reaches the beaker. Sup¬ 
pose that the experiment gave the 
following data: Amount of water 
in the beaker, 400 g. at the begin¬ 
ning, 414.1 g. at the end, including 
the thermal capacity of the beaker 


Figure 316. — Heat of 
Evaporation. 


in terms of water ; temperature at the beginning, 20° C., and at the 
end, 41° C.; observed boiling point, 99° C.; there were 14.1 g. of 
steam condensed. Now, by the principle that the heat lost or given 
off by the steam equals that gained by the water, we have 

400 x (41 - 20) = 14.1 x 7 + 14.1 x (99 - 41) ; 
whence l = 537.7 cal. per gram. 

358. Formation of Dew.—The presence of clouds and the 
“ sweating ” of pitchers filled with ice water show that the 
atmosphere contains water vapor. The amount of water 






HUMIDITY AND HEALTH 


307 


vapor that the atmosphere can hold in suspension depends 
on its temperature. After sunset, if the sky is clear, bodies 
on the earth’s surface, such as grass, leaves, and roots, soon 
cool below the temperature of the surrounding air, and 
water in the form of dew collects on them. Clouds act as 
blankets and prevent the cooling off process, so that little 
or no dew collects. Wind promotes evaporation and dew 
fails to collect. If the temperature falls sufficiently low, 
the dew is deposited as frost. 

359. The Dew Point. — The dew point is the temperature 
at which the aqueous vapor of the atmosphere begins to con¬ 
dense. If water at the temperature of the room be poured 
into a polished nickel-plated beaker and small pieces of ice 
be added with stirring, a mist will soon collect on the out¬ 
side of the beaker. The temperature of the water is then 
the dew point. 

360. Humidity. — The terms dryness and moisture ap¬ 
plied to the air are purely relative. Usually the air is not 
saturated, that is, it does not contain all the water vapor 
it can hold. If it is near the saturation point, it is moist; 
if it is very far from saturation, it is dry. The relative 
humidity of the air is the ratio between the amount of water 
vapor actually present and the amount that would be present 
if the air were saturated at the same temperature. The air 
is saturated at the dew point. A dry day is one on which 
the dew point is much below the temperature of the air; 
a damp day is one on which the dew point is close to the 
temperature of the air. Humidity is expressed as a per 
cent of saturation. 

361. Humidity and Health.—The humidity of the air 
has an important bearing on health. The dry air of a 
furnace-heated house promotes excessive evaporation from 
the bodies of the occupants, producing sensations of chil- 


308 


HEAT 


liness and discomfort. On the other hand, excessive 
humidity retards healthful evaporation, gives a sensation 
of depression, and in hot weather checks Nature’s method 
of keeping cool by evaporation. The humidity conducive 
to health is about 50 per cent. 

Questions and Problems 

1. Why does a drop of alcohol on the hand feel cold? 

2. Why does a shower in summer cool the air? 

3 . Why is there less dew on gravel than on the grass? 

4 . Why can blocks of ice be made to adhere by pressure? 

5 . Why do your eye glasses fog over when you go from the cold 
air outside into a warm room ? 

6. Water in a porous vessel standing in a current of air is colder 
than water in a glass pitcher. Why? 

7 . Why does warming a room make it feel dryer ? 

8. Why does water boil away faster on some days than on others? 

9 . Why does wind dry up the roads after a rain ? 

10. Why does moisture collect on the carburetor of a gasoline 
engine when it is in operation unless it is heated? 

11. How much heat does it take to convert 50 g. of water at 100° 
C. into steam at 100° C.? 

12. How much ice will 100 g. of water at 100° C. melt? 

13 . How much ice will 100 g. of steam at 100° C. melt? 

14 . 100 g. of ice and 20 g. of steam at 100° C. are put into a 

calorimeter. If no heat is lost, what will be the temperature of the 

water after all the ice is melted ? 

15 . How much water at 80° C. will just melt a kilogram of ice? 

16 . How much steam will be required to raise the temperature 
of a kilogram of water from 20° to 50° C. ? 

17 . How much ice will it take to cool a kilogram of water from 
50° to 20° C. ? 

18 . Mt. Washington is 6288 ft. above sea level; at what tempera¬ 
ture does water boil on its top ? 


CONDUCTION 309 

19 . Water boils in the City of Mexico at 92.3° C. What is its 
elevation above the sea? 

20. 50 g. of ice at 0° C. are put into 50 g. of water at 35° C. How 
much of the ice will melt ? 

VI. TRANSMISSION OF HEAT 

362. Conduction. — Twist together two stout wires, iron and cop¬ 
per, of the same diameter, forming a fork with long parallel prongs 



Figure 317.---Difference in Conductivity. 

and a short stem. Support them on a wire stand (Fig. 317), and heat 
the twisted ends. After several minutes find the point on each wire, 
farthest from the flame, where a sulphur match ignites when held 
against the wire. This point will be found farther along on the cop¬ 
per than on the iron, showing that the former has led the heat farther 
from its source. 

Prepare a cylinder of uniform diameter, half of which is made of 
brass and half of wood. Hold a piece of writing paper firmly around 
the junction like a loop (Fig. 318). By applying a Bunsen flame the 
paper in contact with the wood is soon 
scorched, while the part in contact with 
the brass is scarcely injured. The metal 
conducts the heat away and keeps the 
temperature of the paper below the 
point of ignition. The wood is a poor 
conductor. 

These experiments show that 
solids differ in their conductivity 
for heat. The metals are the best 



Figure 318. — Cylinder Half 
Wood, Half Brass. 





310 


HEAT 


conductors ; wood, leather, flannel, and organic substances 
in general are poor conductors*; so also are all bodies in a 
powdered state, owing doubtless to a lack of continuity in 
the material. 

363. Conductivity of Liquids. — Pass a glass tube surmounted 
with a bulb through a cork fitted to the neck of a large funnel. Sup¬ 
port the apparatus as shown in Fig. 319. 
The glass stem should stand in colored 
water. Heat the bulb slightly to expel 
some air, so that the liquid will rise in the 
tube. Fill the funnel with water, covering 
the bulb to the depth of about one centi¬ 
meter. Pour a spoonful of ether on the 
water and set it on fire. The steadiness 
of the index shows that little if any of the 
heat due to the burning ether is conducted 
to the bulb. 

This Experiment shows that water 
is a poor conductor of heat. This 
is equally true of all liquids except 
molten metals. 

364. Conductivity of Gases. — The 

Figure 319.-Water Poor conductivity of gases is very small, 
and its determination is very diffi¬ 
cult because of radiation and convection. The conduc¬ 
tivity of hydrogen is about 7.1 times that of air, while the 
conductivity of water is 25 times as great. 

365. Applications of Conductivity. — If we touch a piece of 
marble or iron in a room, it feels cold, while cloth and wood feel dis¬ 
tinctly warmer. The explanation is that the articles which feel cold 
are good conductors of heat and carry it away from the hand, while 
the poor conductors do not. 

The good heat-conducting property of copper or brass is turned to 
practical account in Sir Humphry Davy’s miner’s lamp (Fig. 320). 






APPLICATIONS OF CONDUCTIVITY 


311 




Figure 320. 
Davy Safety 
Lamp. 


The flame is completely inclosed in metal and fine wire gauze. The 
gauze by conducting away heat keeps any fire damp outside the lamp 
below the temperature of ignition and so prevents ex¬ 
plosions. The action of the gauze is readily illustrated 
by holding it over the flame of a Bunsen burner (Fig. 

321). The flame does not pass through unless the gauze 
is heated to redness. If the gas is first allowed to stream 
through the gauze, it may be lighted on top without 
being ignited below. 

The handles on metal instruments 
that are to be heated are usually made 
of some poor conductor, as wood, bone, 
etc.; or else they are insulated by the 
insertion of some non-conductor, as in 
the case of the handles to silver tea¬ 
pots, where pieces of ivory are inserted 
to keep them from becoming too hot. 

The non-conducting character of air 
is utilized in houses with hollow walls, 
in double doors and double windows, 
and in clothing of loose texture. The warmth of 
woolen articles and of fur is due mainly to the fact 
that much air is inclosed 
within them on account of 
their loose structure. 

The thermos bottle consists of a glass bottle 
with double walls (Fig. 322). The space be¬ 
tween the two walls is exhausted of air, and 
the inner walls of this vacuum are silvered 
to lessen radiation from one to the other. 

Either hot or cold liquids may be kept in a 
thermos bottle with little change of tempera¬ 
ture for several hours. 

The u jireless cooker ” is a box of wood or 
steel with a metallic vessel inside. The two 
are separated by heavy felt or other poorly 
conducting material (Fig. 323). After the 
material to be cooked has been raised to the proper temperature, it is 
placed in the cooker and the latter is tightly closed. The high tem- 


Figure 321.— 
Flame Stopped 
by Wire Gauze. 



Shook Absorber! 


Figure 322. —Thermos 
Bottle. 
































312 


HEAT 


perature is maintained for three hours with a drop of not more than 
10° or 15° C. The cooking may be completed without further appli¬ 
cation of heat. The conductivity of the lining and of the inclosed 

air is so low that heat escapes 
very slowly. Additional heat is 
often supplied by means of hot 
soapstone or cast iron disks. 

366. Convection. — Set up 
apparatus as shown in Fig. 324, 
and support it on a heavy iron 
stand. Fill the flask and connect¬ 
ing tubes with water up to a 
point a little above the open end 
of the vertical tube at C. Apply 
a Bunsen flame to the flask B. A 
circulation of water is set up in 
the apparatus, as shown by the arrows. The circulation is made visible 
by coloring the water in the reservoir blue and that in the flask red. 

The process of conveying heat by the transference of 
the heated matter itself is known as convection. Currents 
set up in this manner are called convection currents. 

367. Heating by Hot Water. — The heating 
of buildings by hot water conveyed by pipes 
to the radiators and thence back again to the 
heater in the basement is an application of 
convection by liquids (Fig. 325). The hot 
water pipe extends to an open tank at the 
top of the building to allow for expansion. 

The circulation is maintained because the hot 
water in the pipes leading to the radiators is 
hotter and therefore lighter than the cooler 
water in the return pipes beyond the ra¬ 
diators. 

368. The Hot Water Heater. — The simplest _ Convect 0N 
arrangement for heating water for general Currents. 












































CONVECTION IN GASES 


313 


domestic purposes is shown 
in Fig. 326. The cold water 
enters the tank at the top 
through a pipe which reaches 
nearly to the bottom. The 
pipe in the bottom leads to 
a heating coil in the gas 
heater. The hot water rises 
and enters the tank at or 
near the top, while heavier 
cold water takes its place 
in the heating coils. The 
circulation thus set up con¬ 
tinues as long as heat is 
applied. 

369. Convection in Gases. — 

Set a short piece of lighted candle 
in a shallow 
beaker and 
place over 
it a lamp 




Heater 


Figure 326. — Water 
Heater. 


i. Figure 325. —Heating by Hot Water. 

chi m n ey. 

Pour into the beaker enough water to close the 
lower end of the chimney. Place in the top of 
the chimney a T-shaped piece of tin as a short 
partition (Fig. 327). If a piece of smoldering 
paper be held over one edge of the chimney, the 
smoke will pass down one side of the partition 
and up the other. If the partition be removed, 
the flame will usually go out. 

Convection currents are more easily 
set up in gases than in liquids. Convec¬ 
tion currents of air on a large scale are 
present near the seacoast. The wind is 













































































































814 


HEAT 


a sea breeze during the day, because the air moves in from 
the cooler ocean to take the place of the air rising over the 
heated land. As soon as the sun 
sets, the ground cools rapidly by 
radiation, and the air over it is 
cooler than over the sea. Hence 
the reversal in the direction of 
the wind, which is now a land 
breeze. 

370. Heating and Ventilating by 
Hot Air. — The hot air furnace 
in the basement is a heater for 
burning wood, coal, distillate, or 
gas, and surrounded by a jacket 
of galvanized iron (Fig. 328). 
Figure 327^-Convection in Cold air f rom outs ide is heated 

between the heater and the jacket 
and rises through the hot air flues to registers in the rooms 
of the building. In houses the extra air often finds an 
outlet through crevices 
and up open chimneys. 

A better way is to 
provide ventilation by 
means of separate flues. 

Since the heated air 
rises to the top of the 
room, it follows that 
if provision is made 
for the escape of the 
colder air by flues at 
the floor, the incom¬ 
ing air will force out 
the foul air, thus Figure 328. — Heating by Hot Air. 





































THE RADIOMETER 


315 


changing the air of the room and warming it at the same 
time. 

Large public buildings must have positive means of 
supplying fresh air to the extent of about 50 cubic feet 
per minute for each person. For this purpose large fans 
driven by power draw in fresh air from the outside and 
force it through flues throughout the building. The air 
is often washed or filtered on its way in, and in cold 
weather is heated by steam pipes. The foul air is forced 
out through openings near the floor. Sometimes exhaust 
fans draw out the vitiated air through the ventilating 
ducts. 

371. Radiation.—When one stands near a hot stove, 
one is warmed neither by heat conducted nor conveyed by 
the air. The heat energy of a hot body is constantly 
passing into space as radiant energy in the ether (§ 243). 
Radiant energy becomes heat again only when it is ab¬ 
sorbed by bodies upon which it falls. Energy transmitted 
in this way is, for convenience, referred to as radiant heat , 
although it is transmitted as radiant energy, and is trans¬ 
formed into heat only by absorption. Radiant heat and 
light are physically identical, but are perceived through 
different avenues of sensation. Radiations that produce 
sight when received through the eye give a sensation of 
warmth through the nerves of touch, or heat a ther¬ 
mometer when incident upon it. The long ether waves 
do not affect the eye, but they heat a body which absorbs 
them. 

372. The Radiometer. — Long heat waves may be de¬ 
tected by the radiometer , an instrument invented by Sir 
William Crookes in 1873 while investigating the properties 
of highly attenuated gases. It consists of a glass bulb 
from which the air has been exhausted until the pressure 


316 


HEAT 



does not exceed 7 mm. of mercury (Fig. 329). Within 
the bulb is a light cross of aluminum wire carrying small 
vanes of mica, one face of each coated with lampblack. 
The whole is mounted to rotate on a vertical pivot. When 
the instrument is placed in the sun¬ 
light or in the radiation from aiiy 
heated body, the cross revolves with 
the blackened faces of the vanes 
moving away from the source of 
heat. 

The infrequent collisions among 
the molecules in such a vacuum pre¬ 
vent the equalization of pressure 
throughout the bulb. The black¬ 
ened sides of the vanes absorb more 
heat than the bright ones, and the 
gas molecules rebound from the 
warmer surfaces with a greater ve¬ 
locity than from the others, thus 
Figure 329.— The Radi- giving the vanes an impulse in the 
opposite direction. This impulse is 
the equivalent of a pressure, which causes the vanes to 
revolve. 


373. Laws of Heat Radiation — Place a radiometer about 50 cm. 
from a small lighted lamp and note the elfect on the radiometer. 
Support a cardboard screen between the lamp and the radiometer; 
the rotation of the radiometer at once becomes slower. 

Hence, Radiation proceeds in straight lines. This law 
is illustrated in the use of fire screens and sunshades. 

Lay a meter stick on a table and place the radiometer at one end 
of it and the lamp at the other. Count the number of revolutions of 
the vanes in one minute. Move the radiometer to a distance of 50 cm. 



HEAT TRANSPARENCY 317 

from the lamp and count the number of revolutions again for a minute. 
It will be about four times as many as before. 

Hence, The amount of radiant energy reeeived by a 
body from any small radiant area varies inversely as 
the square of the distance from it as a source. N ote that 
this law is the same as that relating to the intensity of 
illumination in light (§ 252). 

Support a plane mirror vertically on a table. At right angles to it 
and distant about 5 cm. support a vertical cardboard screen about 
50 cm. long and 20 cm. wide. On one side of this screen place a 
lighted lamp and on the other the radiometer. The vanes will revolve 
rapidly whenever the lamp and the radiometer are in such a position 
that the screen bisects the angle made by lines drawn from them to 
the same point on the mirror. The angles between these lines and 
the screen are the angles of incidence and reflection of the radiant 
energy. 

Hence,* Radiant energy is reflected from a polished sur¬ 
face so that the angles of incidence and reflection are 
equal. 

Select two concave wall lamp reflectors of the same size and blacken 
one of them in the smoke from burning camphor gum. Place a 
lighted lamp about one meter from the radiometer and observe the 
rate of rotation of the vanes. Hold the clear reflector back of the 
radiometer, so as to concentrate the radiation from the lamp upon it, 
and again note the rate of rotation. Now substitute the blackened 
reflector for the clear one; the rate of rotation will be greatly reduced. 

Hence, The capacity of a surface to reflect radiant 
energy depends both on the polish of the surface and on 
the nature of the material. Polished brass is one of the 
best reflectors and lampblack is the poorest. 

374. Heat Transparency. — Select two flat twelve ounce bottles; 
fill one with water and the other with a solution of iodine in carbon 
disulphide. Cut an opening in a sheet of black cardboard of such a 


318 


HEAT 


size that either bottle will cover it. Place this cardboard between the 
lamp and the radiometer and note the effect on the radiometer as the 
opening is closed successively by the bottles. This experiment and 
others similar to it show that 

The transmission of radiant energy through various sub¬ 
stances depends on the temperature of the source , and the 
thickness and nature of the substance itself. 

Substances that transmit a large part of the heat energy, 
such as the solution of iodine and rock salt, are said to be 
diathermanous ; those absorbing a large part, such as water, 
are othermanous. Glass is diathermanous to radiations 
from a source of high temperature, such as the sun, but 
athermanous to radiations from sources of low tempera¬ 
ture, such as a stove. The radiant energy from the sun 
passes readily through the atmosphere to the earth, and 
warms its surface; but the radiations from the-earth are 
stopped to a large extent by the surrounding atmosphere. 
This selective absorption is due in large measure to the 
vapor of water in the air. 

Questions 

1. Why will newspapers spread over plants protect them from 
frost ? 

2. Why does a tall chimney have a stronger draft than a short 
one? 

3. Explain how it is possible to boil water in a paper pail with¬ 
out burning the pail. 

4 . Should the surface of a steam or hot water radiator be rough 
or polished ? 

5 . In what way does a stove heat a room ? 

6. Why does a woolen garment feel warmer than a cotton or a 
linen one ? 

7 . Why is glass an effective screen ? 


HEAT FROM MECHANICAL ACTION 


319 


8. Why does steam burn more severely than hot water? 

9. Why should the registers for removing impure air be placed 
at the floor level ? 

10. What principles of heat are applied in the radiator of an 
automobile ? 

11. Why will the moistened finger or the tongue freeze quickly 
to a piece of very cold iron, but not to a piece of wood? 

12. Why is the boiling point of water in the boiler of a steam 
engine above 100° C. ? 

VII. HEAT AND WORK 

375. Heat from Mechanical Action. — Strike the edge of a 
piece of flint a glancing blow with a piece of hardened steel. Sparks 
will fly at each blow. 

Pound a bar of lead vigorously with a hammer. The 
temperature of the bar will rise. 

In the cavity at the end of a piston of a fire syringe place 
a small piece of tinder, such as is employed in cigar lighters 
(Fig. 330). Force the piston quickly into the barrel. If 
the piston is immediately withdrawn the tinder will prob¬ 
ably be on fire. 

These experiments show that mechanical en¬ 
ergy may be transformed into heat. Some of the 
energy of the descending flint, the hammer, and 
the piston has in each case been transferred to the 
molecules of the bodies themselves, increasing 
their kinetic energy, that is, raising their tern- p rGURE 
perature. 3 3 0 .— 

Savages kindle fire by rapidly twirling a dry Fire Syr - 
stick, one end of which rests in a notch cut in a INGE ‘ 
second dry piece. The axles of carriages and the bearings 
in machinery are heated to a high temperature when not 
properly lubricated. The heating of drills and bits in 
boring, the heating of saws in cutting timber, the burning 









320 


BEAT 


of the hands by a rope slipping rapidly through them, the 
stream of sparks flying from an emery wheel, are instances 
of the same kind of transformation; the work done against 
friction produces kinetic energy in the form of heat. 

376. The Mechanical Equivalent of Heat. — In 1840 Joule 
of Manchester in England began a series of experiments 
to determine the numerical relation between the unit of 
heat and the foot pound. His experiments extended 
over a period of forty years. His most successful method 
consisted in measuring the heat produced when a meas¬ 
ured amount of work was expended in heating water by 
stirring it with paddles driven by weights falling through 
a known height. His final result was that 772 ft.-lb„ 
of work, when converted into heat, raise the temperature 
of 1 lb. of water 1° F., or 1390 ft.-lb. for 1° C. The later 
and more elaborate researches of Rowland in 1879 and of 
Griffiths in 1893 show that the relation is 778 ft.-lb. for 
1°F., or 427.5 kg.-m. for 1° C. ; that is, if the work done 
in lifting 427.5 kg. one meter high is all converted into 
heat, it will raise the temperature of 1 kg. of water 1° C. 
This relation is known as the mechanical equivalent of heat. 
Its value expressed in absolute units is 4.19 x 10 7 ergs 
per calorie. 

377. The Steam Engine.—The most important devices 
for the conversion of heat into mechanical work are the 
steam engine and the gas engine. The former in its 
essential features was invented by James Watt. In the 
reciprocating steam engine a piston is moved alternately 
in opposite directions by the pressure of steam applied 
first to one of its faces and then to the other. This re¬ 
ciprocating or to-and-fro motion is converted into rotatory 
motion by the device of a connecting rod, a crank, and a 
flywheel. 


James Watt (1736-1819) was born at Greenock, Scotland, and 
was educated as an instrument maker. In studying the defects of 

the steam engines then in use, 
he was led to make many 
very important improvements, 
culminating in his invention 
of the double-acting steam 
engine. He invented the ball 
governor, the cylinder jacket, 
the D-valve, the jointed paral¬ 
lelogram for securing recti¬ 
linear motion to the piston, 
the mercury steam-gauge, 
and the water-gauge. He is 
also to be credited with the first 
compound engine, a type of en¬ 
gine extensively used to-day. 


James Prescott Joule (1818-1889), the son of a Manchester 
brewer, was born at Salford, 

England. He became known 
to the scientific world through 
his contributions in heat, elec¬ 
tricity, and magnetism. His 
greatest achievement was es¬ 
tablishing the modern kinetic 
theory of heat by determining 
the mechanical equivalent of 
heat. His experiments on this 
subject were continued 
through a period of forty years. 

In recognition of his great work 
he was presented with the 
Royal Medal of the Royal So¬ 
ciety of England in 1852. 







Row of Corliss Engines, Massachusetts Institute of Technology. 

















THE STEAM ENGINE 


321 


In Fig. 331 are shown in section the cylinder, piston, 
and valve of a slide-valve steam engine. The piston B is 
moved in the cylinder A by the pressure of the steam ad¬ 
mitted through the inlet pipe a. The slide valve d works 
in the steam chest ce 
and admits steam al¬ 
ternately to the two 
ends of, the cylinder 
through the steam 
ports at either end. 

When the valve is 

in the position shown, 

steam passes into the 

right-hand end of the 

cylinder and drives 

the piston toward the 

left. At the same 
.. ., ... Figure 331. — Cylinder of Steam Engine. 

time the other end is 

connected with the exhaust pipe ee through which the 
steam escapes, either into the air, as in a high-pressure 
non-condensing engine , or into a large condensing chamber, 
as in a low pressure condensing engine. 

The slide valve d is moved by the rod i2, connected to 
an eccentric, which is a round disk mounted a little to one 
side of its center, on the engine shaft. It has the effect 
of a crank. The flywheel, also mounted on the shaft of 
the engine, has a heavy rim and serves as a store of energy 
to carry the shaft over the dead points when the piston is 
at either end of the cylinder. There is in the flywheel a 
give-and-take of energy twice every revolution, and a 
fairly steady rotation of the shaft is the result. 

The eccentric is set in such a way that the rod R closes 
the valve admitting steam to either end of the cylinder 


















322 


HEAT 


before the piston has completed its stroke; the motion of 
the piston is continued during the remainder of the stroke 
by the expansive force of the steam. 

Corliss valves are commonly used in large slow speed 
engines. As distinguished from the slide valve, the 
Corliss valve is cylindrical and opens and closes by turn¬ 
ing a little in its seat, first in one direction and then the 
other. In the Corliss engine there are four such valves, two 
at each end of the steam cylinder. One of each pair admits 
steam to the cylinder and the other is the exhaust valve. 
When the inlet valve is open at one end of the steam cylin¬ 
der, the exhaust valve is open at the other end. All four 
valves are opened and closed automatically by the motion of 
the engine itself. Each valve can be adjusted separately. 



378. The Indicator Diagram. — The steam indicator is a device 
for the automatic tracing of a diagram representing the relation be¬ 
tween the volume and the pressure of the steam 
in the cylinder during one stroke. This dia¬ 
gram is known as an “ indicator card ” (Fig. 
332). 

From a to b the inlet port 
is open and the full pressure 
of steam is on the piston ; at 
b the inlet port closes and 
the steam expands from b to 
c, when the exhaust port opens; at d the pressure is reduced to 
the lowest value and remains sensibly constant during the return 
movement of the piston until e is reached, when the exhaust port 
closes and the remaining steam is compressed from e to f At / the 
inlet port opens and the pressure rises abruptly to the initial maxi¬ 
mum, thus completing the cycle. The work done during the stroke 
is represented by the inclosed area abcdef. The indicator card is used 
also in adjusting the valves. 


Volume 

Figure 332. — Indicator Diagram. 


379. The Steam Turbine. —The steam turbine has the 
great advantage of producing rotary motion directly with- 










- 


U'T 




X:>. 


A: 








A 4-Valve Engine Directly Connected to a Dynamo-electric Machine. 











Above : Section through the Steam Turbine, showing Nozzles and Buckets. 
Below: The Rotor of a Turbine, showing Buckets Increasing in Size 

from Left to Right. 









THE GAS ENGINE 


323 


out the intervention of a connecting rod and crank to 
convert the back and forth motion of the piston in a 
reciprocating engine into rotary motion. In the latter 
the piston stops and starts again twice during each revo¬ 
lution of the flywheel, and the stopping and starting gives 
rise to disagreeable vibrations. In the steam turbine the 
rotor revolves continuously and the impulses it receives 
are constant instead of intermittent. 

Steam enters the turbine through a set of stationary 
nozzles, shown in section in the half tone. Here it expands 
and acquires a high velocity. It then strikes the entrance 
edge of the first row of buckets in the rotor, gives up en¬ 
ergy to them, and drives them forward as it passes 
through. It then passes through the second set of sta¬ 
tionary nozzles, of greater area than the first; here it 
again expands, increases its velocity, and enters the second 
row of buckets. The process is repeated in successive 
stages until it reaches the exhaust outlet. By its im¬ 
pulse on each row of buckets it gives up energy to the 
rotor. The half tone of a complete rotor shows the in¬ 
creasing size of the buckets from left to right. The 
buckets are curved openings through the rotor, as shown 
in section in the half tone. 

380. The Gas Engine. — The gas engine is a type of in¬ 
ternal combustion engine , which includes motors using gas, 
gasoline, kerosene, or alcohol as fuel. The fuel is intro¬ 
duced into the cylinder of the engine, either as a gas or as 
a vapor, mixed with the proper quantity of air to produce a 
good explosive mixture. The mixture is ignited at the 
right instant by means of an electric spark. The explo¬ 
sion and the expansive force of the hot gases drive the 
piston forward in the cylinder. 

In th q four-cycle type of gas engine, the explosive mix- 


324 


BEAT 


ture is drawn in and ignited in each cylinder only every 
other revolution of the engine, while in the two-cycle type 
an explosion occurs every revolution. The former type 
is used in most motor car engines, and the latter in small 
motor boats. 

The operation of a four-cycle engine is illustrated in 1, 
which shows the four steps in a 
complete cycle. The inlet valve 
a and the exhaust valve b are 
operated by the cams c and d. 
Both valves are kept normally 
closed by springs, surrounding the 
valve stems. The small shafts to 
which the two cams are fixed are 
driven by the spur wheel e on 
the shaft of the engine. This 
wheel engages with the two larger 
spur wheels on the cam shafts, 
each having twice as many teeth 
as e and forming with it a two- 
to-one gear, so that c and d rotate 
once in every two revolutions of 
the crank shaft. The piston m 
has packing rings; h is the con¬ 
necting rod, k the crank shaft, and l the spark plug. 

In diagram 1 the piston is descending and draws in the 
charge through the open valve a ; in 2 both valves are 
closed and the piston compresses the explosive charge ; 
about the time the piston reaches its highest point, the 
charge is ignited by a spark at the spark plug, and the 
working stroke then takes place, as in 3, both valves 
remaining closed ; in 4 the exhaust valve b is opened by 
the cam d , and the products of the combustion escape 


2, 3, and 4 of Fig. 333, 



Figure 333. — Showing Four 
Steps in Cycle. 





















































































1 vVHR 

1 

r * 

1 

I 



* 


Front and Rear Views of an Aerial “Flivver.” 
One of the smallest practical airplanes made. 












THE AIRPLANE 


325 


through the muffler, or directly into the open air. The 
piston has now traversed the cylinder four times , twice in 
in each direction, and the series of operations begins again. 

381. Two-Cycle Engine, — Figure 334 is a section of a 
two-cycle gas engine. During the up-stroke of the piston 
P a charge is drawn through A into the crank case 0. 
At the same time a charge in the cylinder is compressed 
and is ignited by a spark when the 
compression is greatest. The piston 
is forced down, and when it passes 
the port E the exhaust takes place. 

When the admit port I is passed, 
a charge enters from the crank 
case. To prevent this charge from 
passing across and escaping at E , it 
is made to strike against a projec¬ 
tion B on the piston, which deflects 
it upward. The momentum of the 
balance wheel carries the piston up¬ 
ward, compresses the charge, and 
draws a fresh charge into the crank 
case. The piston has now traversed 
the cylinder twice , once in each direction, and the same 
series of operations is again repeated. 

For a more complete discussion of gas engines and auto¬ 
mobiles, see Chapter XV, page 460. 

382. The Airplane. —The principle of the airplane has 
already been described in § 124. It is a 44 heavier than 
air ” machine and is lifted as the kite is lifted; but instead 
of the wind blowing against it, it is forced against the air 
by a powerful gas engine, driving a high speed propeller. 
Formerly the engine and the propeller were at the rear 
end, but recent practice is to mount them in front. 



Two-Cycle Engine. 










326 


HEAT 


Questions and Problems 

1. Why does the temperature of the air under the bell jar of an 
air pump fall when the pump is worked ? 

2 . Is there a difference in the temperature of the steam as it enters 
a steam engine and as it leaves at the exhaust ? Explain. 

3. Lead bullets are sometimes melted when they strike a target. 
Explain. 

4. Does clothing keep the cold out or keep the heat in? 

5. Is there any less moisture in the air after it has passed through 
a heated furnace into a room than there was before? 

6. Why does the rapid driving of an automobile heat the air in 
the tires? 

7. A mass of 200 g. moving with a speed of 50 m. per second is 
suddenly stopped. If all its energy is converted into heat, how many 
calories would be generated ? 

Note. A calorie equals 4.19 x 10 7 ergs. 

8 . If all the potential energy of a 300 kg. mass of rock is con¬ 
verted into heat by falling vertically 200 m., how many calories would 
be generated? 

9. How high could a 200 g. weight be lifted by the heat required 
to melt the same mass of ice, if all the heat could be utilized for the 
purpose ? 

10 . If the average pressure of steam in the cylinder of an engine is 
100 lb. per square inch, the area of the piston is 80 sq. in., and the 
stroke 1 ft., how many horse powers would be developed if the 
engine makes two revolutions per second ? 


CHAPTER X 


MAGNETISM 

X. MAGNETS AND MAGNETIC ACTION 

383. Natural Magnets or Lodestones. —Black oxide of 
iron, known to mineralogists as magnetite , is found in many 
parts of the world, notably in Arkansas, the Isle of Elba, 
Spain, and Sweden. Some of these hard black stones are 
found to possess the property of attracting to them small 
pieces of iron. At a very early date such pieces of iron 
ore were found near Magnesia in Asia Minor, and they 
were therefore called magnetic stones and later magnets. 
They are now known as natural magnets, and the properties 
peculiar to them as magnetic properties. 

Dip a piece of natural magnet into iron filings; they will adhere 
to it in tufts, not uniformly over its surface, but chiefly at the* ends 
and on projecting edges (Fig. 335). 

Suspend a piece of natural magnet by a 
piece of untwisted thread (Fig. 336), or float 
it on a wooden raft on water. Note its posi- 

tion, then disturb it Figure 335. -Natural 
slightly, and again let it Magnet. 

come to rest. It will be found that it invariably 
returns to the same position, the line connecting 
the two ends to which the filings chiefly adhered 
in the preceding experiment lying north and 
south. 

This directional property of the natu¬ 
ral magnet was early turned to account 

327 





328 


MAGNETISM 


in navigation, and secured for it the name of lodestone 
(leading-stone). 

384. Artificial Magnets. — Stroke the blade of a pocket knife 
from end to end, and always in the same direction, with one end of a 
lodestone. Touch it to iron filings; they will cling to its point as 
they did to the lodestone. The knife blade has become a magnet. 

Use the knife blade of the last experiment to stroke another blade. 
This second blade will also acquire magnetic properties, and the first 
one has suffered no loss. 

Artificial magnets , or simply magnets, are bars of hard¬ 
ened steel that have been made magnetic by the applica¬ 
tion of some other magnet or magnetizing force. The 
form of artificial magnets most commonly met with are 
the bar and the horseshoe. 

385. Magnetic Substances. — Any substance that is at¬ 
tracted by a magnet or that can be magnetized is a mag¬ 
netic substance. Faraday showed that most substances 
are influenced by magnetism, but not all in the same way 
nor to the same degree. Iron, nickel, and cobalt are 
strongly attracted by magnets and are said to be mag¬ 
netic; bismuth, antimony, phosphorus, and copper act as 
if they are repelled by magnets and they are called dia¬ 


magnetic. Most of the alloys 
of iron are magnetic, but 



Figure”337. — Magnet Tufted with manganese steel is non-mag- 


netic. 


Iron Filings. 


386. Polarity. — Roll a bar magnet in iron filings. It will be 
come thickly covered with the filings near its end. Few, if any, will 
adhere at the middle (Fig. 337). 

The experiment shows that the greater part of the mag¬ 
netic attraction is concentrated at or near the ends of the 
magnet. They are called its poles, and the magnet is said 


MAGNETIC TRANSPARENCY 


329 



Figure 338. — Floating Magnet. 


to have polarity. The line joining the poles of a long 
slender magnet is its magnetic axis. 

387. North and South Poles. —Straighten a piece of watch 
spring 8 or 10 cm. long, stroke it from end to end with a magnet, and 
float it on a cork in a 

vessel of water (Fig. 

338). It will turn from 
any other position to a 
north and south one, 
and invariably with the 
same end north. 

The end of a magnet 

pointing toward the north is called the north-seeking pole, and the other, 
the south-seeking pole. They are commonly called simply the north pole 
and the south pole. 

388. Magnetic Needle. — A slender magnetized bar, sus¬ 
pended by an untwisted fiber or pivoted on a point so as 
to have freedom of motion about a vertical axis is a mag¬ 
netic needle (Fig. 339). The 
direction in which it comes to 
rest without torsion or friction 
is called the magnetic meridian. 

Fasten a fiber of unspun silk to 
a piece of magnetized watch spring 
about 2 cm. long so that it will hang 
horizontally. Suspend it inside a 
wide-mouthed bottle by attaching 
the fiber to a cork fitting the mouth 
of the bottle. The little magnetic 
needle will then be protected from 
currents of air. It may be made visible at a distance by sticking fast 
to it a piece of thin white paper. 

389. Magnetic Transparency. — Cover the pole of a strong bar 
magnet with a thin plate of glass. Bring the face of the plate oppo¬ 
site the pole in contact with a pile of iron tacks. A number will be 



Figure 339. — Magnetic Needle. 





830 


MAGNETISM 


found to adhere, showing that the attraction takes place through 
glass. In like manner, try thin plates of mica, wood, paper, zinc, 
copper, and iron. No perceptible difference will be seen except jn 
the case of the iron, where the number of tacks lifted will be much 
less. 

Magnetic force acts freely through all substances except 
those classified as magnetic. Soft iron serves as a more or 
less perfect screen to magnetism. Watches may be pro¬ 
tected from magnetic force that is not too strong by means 
of an inside case of soft sheet iron. 

390. First Law of Magnetic Action. — Magnetize a piece of 
large knitting needle, about four inches long, by stroking it from the 
middle to one end with the north pole of a bar magnet, and then 
from the middle to the other end with the south pole. Repeat the 
operation several times. Present the north pole of the magnetized 
knitting needle to the north pole of the needle suspended in the 
bottle. The latter will be repelled. Present the same pole to the 
south pole of the little magnetic needle; it will be attracted. Repeat 
with the south pole of the knitting needle and note the deflections. 

The results may be expressed by the following law of 
magnetic attraction and repulsion : 

Lilce magnetic poles repel and unlike magnetic poles 
attract each other. 

391. Testing for Polarity. —The magnetic needle affords 
a ready means of ascertaining which pole of a magnet is 
the north pole, for the north pole of the magnet is the one 
that repels the north pole of the magnetic needle. Repul¬ 
sion is the only sure test of polarity for reasons that will 
appear in the experiments that follow. 

392. Induced Magnetism. — Hold vertically a strong bar magnet 
and bring up against its lower end a short cylinder of soft iron. It 
will adhere. To the lower end of this one attach another, and so on 


UNLIKE POLARITY INDUCED 


331 


in a series of as many as will stick (Fig. 340). Carefully detach the 
magnet from the first piece of iron and withdraw it slowly. The 
pieces of iron will all fall apart. 


The small bars of .iron hold together 
because they become temporary mag¬ 
nets. Magnetism produced in mag¬ 
netic substances by the influence of a 
magnet near by or in contact with 
them is said to be induced, and the 
action is called magnetic induction. 
Magnetic induction precedes attrac¬ 
tion. 



Figure 340. — Induced 
Magnetism. 


393. Unlike Polarity Induced. —- Place a bar magnet in line 
with the magnetic axis of a magnetic needle, with its north pole as 
near as possible to the north pole of the needle without appreciably 
repelling it (Fig. 341). Insert a bar of soft iron between the magnet 
^ and the needle. The north pole 

of the needle will be immedi¬ 
ately repelled. 



The repulsion of the 

north pole of the needle by 
F.oure 341.- Polarity by Induct,on. the end of the goft iron bar 

next to it shows that this end of the bar has acquired 
a polarity the same as that of the magnet, that is, north 
polarity. Then the other end adjacent to the magnet 
must have acquired the opposite polarity. 

When a magnet is brought near a piece of iron, the iron 
is magnetized by induction, and there is attraction because 
the adjacent poles are unlike. When a bunch of iron fil¬ 
ings or tacks adhere to a magnet, each filing or tack be¬ 
comes a magnet and acts inductively on the others and all 
become magnets. Weak magnets may have their polarity 
reversed by the inductive action of a strong magnet. 




832 


MAGNETISM 


394. Permanent and Temporary Magnetism. — When a 

piece of hardened steel is brought near a magnet, it 
acquires magnetism as a piece of soft iron does under 
the same conditions: but the steel retains its magnetism 
when the magnetizing force is withdrawn, while the soft 
iron does not. In the experiment of § 392 the soft iron 
ceases to be a magnet when removed to a distance from 
the bar magnet. In addition, therefore, to the permanent 
magnetism exhibited by the magnetized steel, we have 
temporary magnetism induced in a bar of soft iron when it 
is brought near a magnet or in contact with it. 


II. NATURE OF MAGNETISM 


Figure 342. — Bent Magnet. 


395. Magnetism a Molecular Phenomenon. — If a piece of 
watch spring be magnetized and then heated red hot, it will lose its 
magnetism completely. 

A magnetized knitting needle will not pick up as many tacks after 
being vibrated against the edge of a table as it did before. 

A piece of moderately heavy and very 
soft iron wire of the form shown in 
Fig. 342 can be magnetized by stroking 
it gently with a bar magnet. If given 
a sudden twist, it loses at once all the magnetism imparted to it. 

A piece of watch spring attracts iron filings only at its ends. If 
broken in two in the middle, each half will be a magnet and will 
attract filings, two new poles having been formed where the original 
magnet was neutral. If these pieces in turn be broken, their parts 
will be magnets. If this division into separate magnets be conceived 
to be carried as far as the molecules, they too would probably be 
magnets. 


It is worthy of notice that magnetization is facilitated 
by jarring the steel, or by heating it and letting it cool 
under the influence of a magnetizing force. If an iron 
bar is rapidly magnetized and demagnetized, its tempera¬ 
ture is raised. A steel rod is slightly lengthened by 




MAGNETIC FIELDS 


magnetization and a faint click may be heard if 
the magnetization is sudden. 

396. Theory of Magnetism. — The facts of the 
preceding section indicate that the seat of mag¬ 
netism is the molecule, that the individual mole¬ 
cules are magnets, that in an unmagnetized 
piece of iron the poles of the molecular magnets 
are turned in various directions, so that they 
form stable combinations or closed magnetic 
chains, and hence exhibit no magnetism external 
to the bar (Fig. 343). In a magnetized bar the 
larger portion of the molecules have 
their magnetic axes pointing in the same 
direction (Fig. 344), the completeness 
of the magnetization depending on the complete¬ 
ness of this alignment. 

III. THE MAGNETIC FIELD 

397. Lines of Magnetic Force. — Place a sheet of 
paper over a small bar magnet and sift iron filings evenly 
over it from a bottle with a piece of gauze tied over the 
mouth, tapping the paper gently to aid the filings in ar¬ 
ranging themselves under the influence of the magnet. 
They will cling together in curved lines, which diverge 
from one pole of the magnet and meet again at the oppo¬ 
site pole. 

These lines are called lines of magnetic force or of mag¬ 
netic induction . Each particle of iron becomes a magnet 
by induction; hence the lines of force are the lines along 
which magnetic induction takes place. 

398. Magnetic Fields. — A magnetic field is the space 
around a magnet in which there are lines of magnetic 
force. 


BBBB 

BBSS 

BBSS 

flflBfi 

BBBB 

BBBB 

BBBB 

BBBB 

BBBB 

BBBB 

BBBB 

BBBB 

BBBB 


Figure 
344. — 
Magnet¬ 
ized Bar. 


333 


can oca 

n 

on na 
*>t>*?<* 


Figure 

343.— 

Unmag¬ 

netized 

Bar. 





334 


MAGNETISM 


Figure 345 was made from a photograph of the magnetic field of a 
bar magnet in a plane passing through the magnetic axis. These 
lines branch out nearly radially from one pole and curve round 
through the air to the other pole. Faraday gave to them the name 



Figure 345. — Magnetic Field of Bar Magnei. 


lines offorce. The curves made by the iron filings “represent visibly 
the invisible lines of magnetic force.” 

Figure 34C shows the field about two bar magnets placed with their 
unlike poles adjacent to each other. Many of the lines from the north 
pole of the one extend across to the south pole of the other, and this 

connection denotes at¬ 
traction. 

Figure 347 shows the 
field about two bar mag¬ 
nets with their like poles 
adjacent to each other. 
None of the lines spring¬ 
ing from either pole ex¬ 
tend across to the neigh¬ 
boring pole of the other 
magnet. This is a pic- 
Figure 346. — Magnetic Field, Two Unlike ture °f magnetic repul- 
Poles. sion. 

399. Properties of Lines of Force. — Lines of magnetic 
force have the following properties: (a) They are under 
tension, exerting a pull in the direction of their length; 









PERMEABILITY 


335 


(5) they spread out as if repelled from one another at 
right angles to their length; (<?) they never cross one 
another. 

400. Direction of 
Lines of Force. — 

Hold a mounted magnetic 
needle about 1 cm. long 
near a bar magnet. It 
will place itself tangent 
to the line of force passing 
through it. 

Suspend by a fine 
thread about 60 cm. long 
a strongly magnetized 
sewing needle with its north pole downward. Bring this pole of the 
needle over the north pole of a horizontal bar magnet (Fig. 348). It 
will be repelled and will move along a curved line of force toward the 
south pole of the magnet. 



Poles. 


The direction of a line of force at any point is that of 
a line drawn tangent to the curve at that point, and the 



positive direction is 
that in which a north 
pole is urged. Since 
the north pole of a 
magnetic needle is re¬ 
pelled by the north 
pole of a bar magnet, 
an observer standing 
with his back to the 
north pole of a mag¬ 
net looks in the di¬ 
rection of the lines of force coming from that pole. 


Figure 348. — Direction of Lines of Force. 


401. Permeability. — Place a piece of soft iron near the pole of 
a bar magnet and map out the field with iron filings. The lines are 
displaced by the iron and are gathered into it (Fig. 349). 












336 


MAGNETISM 


When iron is placed in a magnetic field, the lines of 
force are concentrated by it. This property possessed by 

iron, when placed 
in a magnetic 
field, of concen¬ 
trating the lines 
of force and in¬ 
creasing their 
number, is known 
as permeability. 
The superior per¬ 
meability of soft 
Figure 349. - Displacement of Lines. iron exp l ains t he 

action of magnetic screens (§ 389). In the case of the 
watch shield, the lines of force follow the iron and do not 
cross it; the watch is thus protected from, magnetism be¬ 
cause the lines of force do not pass through it except when 
the magnetic field is very strong. 



IV. TERRESTRIAL MAGNETISM 


402. The Earth a Magnet. — Support a thoroughly annealed 
iron rod or pipe horizontally in an east-and-west line and test it for 
polarity. It should show no magnet¬ 
ism. Now place it north and south 
with the north end about 70° below 
the horizontal (Fig. 350). While in 
this position, tap it with a hammer 
and then test it for polarity. The 
lower end will be found to be a north 
pole and the upper end a south pole. 

Turn the rod end for end, hold in the 
former position, and tap again with a 
hammer. The lower end will again 
become a north pole ; the magnetism Figure 350. — Earth Induceo 
has been reversed. Magnetism. 






MAGNETIC DIP 


337 


This experiment shows that the earth acts as a magnet 
on the iron rod and magnetizes it by induction. Similarly, 
iron objects, such as a stove, a radiator, vertical steam 
pipes, iron columns, and hitching 
posts, become magnets with the 
lower end a north pole. The in¬ 
ductive action of the earth as a 
magnet accounts for the magnet¬ 
ism of natural magnets. 



am mr rr,, , , Figure 351. — Magnetic Dip. 

403. Magnetic Dip. — Thrust two 

unmagnetized knitting needles through a cork at right angles to each 
other (Fig. 351). Support the apparatus on the edges of two glasses, 
with the axis in an east-and-west line, and the needle adjusted so as 
to rest horizontally. Now magnetize the needle, being careful not to 
displace the cork. It will no longer assume a horizontal position, the 
north pole dipping down as if it had become 
heavier. 



Figure 352. — Dipping 
Needle. 


The inclination or dip of a needle is 
the angle its magnetic axis makes with 
a horizontal plane. A needle mounted 
so as to turn about a horizontal axis 
through its center of gravity is a dip¬ 
ping needle (Fig. 352). The dip of 
the needle at the magnetic poles of the 
earth is 90°, at the magnetic equator, 
0°. In 1907 Amundsen placed the 
magnetic pole of the northern hemi¬ 
sphere in latitude 75° 5' N. and longi¬ 
tude 96° 47' W. The magnetic pole 
of the southern hemisphere is probably near latitude 
72° S. and longitude 155° E. 

Isoclinic lines are lines on the earth’s surface passing 
through points of equal dip. They are irregular in di- 



338 


MAGNETISM 


rection, though resembling somewhat parallels of lati¬ 
tude. 

404. Magnetic Declination. — The magnetic poles of the 
earth do not coincide with the geographical poles, and 
consequently the direction of the magnetic needle is not 
in general that of the geographical meridian. The angle 
between the direction of the needle and the meridian at 
any place is the magnetic declination. To Columbus be¬ 
longs the undisputed discovery that the declination is dif¬ 
ferent at different points on the earth’s surface. In 1492 
he discovered a place of no declination in the Atlantic 
Ocean north of the Azores. The declination at any place 
is not constant, but changes as if the magnetic poles oscil¬ 
late, while the mean position about which they oscillate 
is subject to a slow change of long period. The annual 
change on the Pacific coast is about 4', and in New Eng¬ 
land about 3'. At London in 1657 the magnetic declina¬ 
tion was zero, and it attained its maximum westerly 
value of 24° in 1816 ; in 1915 it was 15° 19' W. 

405. Agonic Lines. — Lines drawn through places where 
the needle points true north are called agonic lines. In 
1910 the agonic line in North America ran from the mag¬ 
netic pole southward across Lake Superior, thence near 
Lansing, Michigan, Columbus, Ohio, through West Vir¬ 
ginia and South Carolina, and it left the mainland near 
Charleston on its way to the magnetic pole in the south¬ 
ern hemisphere. East of this line the needle points west 
of north; west of it, it points east of north. Lines pass¬ 
ing through places of the same declination are called 
isogonic lines. 


QUESTIONS 


339 


Questions 

1. Given a bar magnet of unmarked polarity; determine which 
end is its north pole. 

2. Out of a group of materials, how would you select the mag¬ 
netic substances? 

3 . Given two bars exactly alike in appearauce, one soft iron and 
the other hardened steel. Select the steel one by means of magnetism. 

4 . Magnetize a long darning needle, then break it in the middle. 
Will there be two magnets, each with one pole? 

5 . How would you magnetize a sewing needle so that the eye is 
the north pole ? 

6. What effect would it have on a compass to place it within an 
iron kettle? 

7 . Will an iron fence post standing in the ground have any in¬ 
fluence on the needle of a surveyor’s compass ? 

8. Float a magnet on a cork. Will the earth’s magnetism cause 
it to float toward the earth’s magnetic pole? 

9. Is the polarity of the earth’s magnetism in the northern hemi¬ 
sphere the same as that of the north pole of a magnet ? 

10. Suppose you wish to make a magnetic needle. If it is bal¬ 
anced on a point so as to rest in a horizontal position before magnet¬ 
ization, will it rest horizontally after it is magnetized ? 


CHAPTER XI 


ELECTROSTATICS 
I. ELECTRIFICATION 


406. Electrical Attraction. — Rub a dry flint glass rod with a 

silk pad and bring it near a pile of pith balls, bits of paper, or chaff. 

They will at first be at¬ 
tracted and then repelled 
(Fig. 353). 




Figure 353. — Electrical Attraction. 


The simple fact that 
a piece of amber (a fos¬ 
sil gum) rubbed with 
a flannel cloth acquires 
the property of at¬ 
tracting bits of paper, 
pith, or other light 
bodies, has been known since about 600 B.C.; but it seems 
not to have been known down to the time of Queen Eliza¬ 
beth that any bodies except amber and jet were capable of 
this kind of excitation. About 1600 Dr. Gilbert dis¬ 
covered that a large number of substances, such as glass, 
sulphur, sealing wax, resin, etc., possess the same peculiar 
property. These he called electrics (from the Greek word 
for amber, electron). A body excited in this manner is 
said to be electrified , its condition is one of electrification , 
and the invisible agent to which the phenomenon is re¬ 
ferred is electricity . 


340 




TWO KINDS OF ELECTRIFICATION 


341 


407. Electrical Repulsion. — Suspend several pith balls from a 
glass hook (Fig. 354). Touch them with an electrified glass tube. 
They are at first attracted but they soon fly away from the tube and 
from one another. When the tube is 
removed to a distance, the balls no 
longer hang side by side, but keep apart 
for some little time. If we bring the 
hand near the balls they will move 
toward it as if attracted, showing that 
the balls are electrified. 



From this experiment it ap¬ 
pears that bodies become elec¬ 
trified by coming in contact with 
electrified bodies, and that elec¬ 
trification may show itself by re¬ 
pulsion as well as by attraction. 


Figure 354. — Electrical 
Repulsion. 



408. Attraction Mutual. — Electrify a flint glass tube by fric¬ 
tion with silk, and hold it near the end of a long wooden rod resting 
in a wire stirrup suspended by a silk thread (Fig. 355). The sus¬ 
pended rod is attracted. Now, replace the rod by the electrified tube. 

When the rod is held near the rubbed end 
of the glass tube, the latter moves as if at¬ 
tracted by the former. 

The experiment teaches that each 
body attracts the other; that is, the 1 
action is mutual. 

409. Two Kinds of Electrification. — 

Rub a glass tube with silk and suspend it 
as jn Fig. 355. Rub a second glass tube 
and hold it near one end of the suspended 
one. The suspended tube will be repelled. Bring near the sus¬ 
pended tube a rod of sealing wax rubbed with flannel. The suspended 
tube is now attracted. Repeat these tests with an electrified rod of 
sealing wax in the stirrup instead of the glass tube. The electrified 



Figure 355. — Attrac¬ 
tion Mutual. 




342 


ELECTROSTA TICS 


sealing wax will repel the electrified sealing wax, but there will be 
attraction between the sealing wax and the glass tube. 

The experiment illustrates the fact that there are two 
kinds of electrification: one developed by rubbing glass 
with silk, and the other by rubbing sealing wax with 
flannel. To the former Benjamin Franklin gave the name 
positive electrification ; to the latter, negative electrification. 

It appears further that bodies charged with the same 
kind of electrification repel each other, and bodies charged 
with unlike electrifications attract each other. Hence the 
law: 

Like electrical charges repel each other; unlike electri¬ 
cal charges attract each other- 


w. 


W- 


410. The Electroscope. — An instrument for detecting electri¬ 
fication and for determining its kind is called an electroscope. Of the 
many forms proposed the one shown in section in 
Fig. 356 is typical. The indicating system consists 
of a rigid piece of brass J3, to which is attached a 
narrow strip of gold leaf G. This system is supported 
by a block of sulphur 1 , which in turn is suspended 
by a rod fitting tightly in a block of ebonite E. A 
charging wire W passes through the ebonite and is 
bent at right angles at the bottom. By rotating the 
upper bent end of W, the arm at the bottom may be 
brought in contact with the brass strip for charging. 
Instead of a ball the supporting rod may end in a 
round flat plate. When the instrument has flat 


Figure 356. — 
Electroscope. 


sides, the gold leaf may be projected on the screen with a 
lantern. 



Figure 357. — Proof Plane. 


411. Charging an Electro¬ 
scope. — To charge an electroscope 
an instrument called a proof plane 
is needed. It consists of a small metal disk attached to an ebonite 
handle (Fig. 357). To use it, touch the disk to the electrified body 
and then apply it to the knob of the electroscope. The angular 










CONDUCTORS AND NONCONDUCTORS 


343 


separation of the foil from the stem will indicate the intensity of the 
electric charge imparted. This method is known as charging by 
contact in distinction from charging by induction to be described later. 

412. Testing for Kind of Electrification. — Charge the 
electroscope, by means of the proof plane, with the kind 
of electrification to be identified, until the leaf diverges a 
moderate distance. Then apply a charge from a glass rod 
electrified by rubbing with silk. If the divergence in¬ 
creases, the first charge was positive; if not, recharge the 
electroscope from the unknown and apply a charge taken 
from a stick of sealing wax excited by friction with flan¬ 
nel. No certain conclusion can be drawn unless an in¬ 
creased divergence is obtained. 

413. Conductors and Nonconductors. — Fasten a smooth metal 
button to a rod of sealing wax and connect the button with the knob 
of the electroscope by a fine copper wire, 50 to 100 cm. long. Hold 
the sealing wax in the hand and touch the button with an electrified 
glass rod. The divergence of the leaf indicates that it is electrified. 
Repeat the experiment, using a silk thread instead of the wire; no 
effect is produced on the electroscope. Now wet the thread with 
water and apply the electrified rod; the effect is the same as when the 
wire was used. 

It is clear from these experiments that electric charges 
pass readily from one point to another along copper wire, 
but do not pass along dry silk thread. It is therefore cus¬ 
tomary to divide substances into two classes, conductors 
and nonconductors , or insulators, according to the facility 
with which electric charges pass in them from point to 
point. In the former if one point of the body is electrified 
by any means, the electrification spreads over the whole 
body, but in a nonconductor the electrification is confined 
to the vicinity of the point where it is excited. Sub¬ 
stances differ greatly in their conductivity, so that it is 


844 


ELECTROSTATICS 


not possible to divide them sharply into two classes. 
There is no substance that is a perfect conductor; neither 
is there any that affords perfect insulation. Metals, car¬ 
bon, and the solution of some acids and salts are the best 
conductors. Among the best insulators are paraffin, tur¬ 
pentine, silk, sealing wax, India rubber, gutta-percha, dry 
glass, porcelain, mica, shellac, spun quartz fibers, and 
liquid oxygen. Some insulators, like glass, become good 
conductors when heated to a semi-fluid condition. 


II. ELECTROSTATIC INDUCTION 



414. Electrification by Induction. — Rub a glass tube with silk 
and bring it near the top of an electroscope. The leaves begin to 

diverge when the tube is some dis¬ 
tance from the knob (Fig. 358) and 
the amount of divergence increases 
as the tube approaches. When 
the tube is removed the leaves col- 


Since the leaves do not re¬ 
main apart, it is evident that 
there has been no transfer of 
electrification from the tube 
to the electroscope. The 
electrification produced in 
the electroscope when the 
electrified body is brought 
near it is owing to electrostatic 
induction. This form of elec¬ 
trification is only a temporary one and it is brought about 
by the presence of a charged body in its vicinity. 


Figure 358. — Electrification 
Induction. 


415. Sign of the Induced Charges. — Lay a smooth metallic 
ball on a dry plate of glass. Connect it with the knob of the electro- 





EQUALITY OF TUE TWO CHARGES 


345 


scope by means of a stout wire with an insulating handle (Fig. 359). 
The ball and the electroscope now form one continuous conductor. 
Bring near the ball an electrified glass tube; the leaves of the elec¬ 


troscope diverge. Before with¬ 
drawing the excited tube, remove 
the wire conductor. The electro¬ 
scope remains charged, and it will 
be found to be positive. A similar 
test made of the ball will show that 
it is negatively charged. 



Figure 359. — Wire with Insu¬ 
lating Handle. 


Hence, we learn that when an electrified body is brought 
near an object it induces the opposite kind of electrification 
on the side next it and the same kind on the remote side. 


416. Charging an Electroscope by Induction. — Hold a finger 


on the ball of the electroscope and bring near it an electrified glass 
tube (Fig. 360). Remove the finger before taking away the tube; the 

electroscope will be charged 
negatively. If a stick of elec¬ 
trified sealing wax be used in¬ 
stead of the glass tube, the 
electroscope will be charged 
positively. 

417. Equality of the Two 
Charges. — Using the appa¬ 
ratus of § 415, charge the 
ball and the electroscope by 
induction. Then replace the 
wire conductor. The leaves 
of the electroscope will col¬ 
lapse, showing that the elec¬ 
troscope is discharged. If the 
ball be tested, it will also 
be found to be discharged. 
Hence, 



Figure 360. — Charging Electroscope 
by Induction. 


The inducing and the induced charges are equal to each 
other. 







346 


ELECTROSTA TICS 


III. ELECTRICAL DISTRIBUTION 




418. The Charge on the Outside of a Conductor. — Place a 
round metallic vessel of about one liter capacity on an insulated 

support (Fig. 361). Electrify 
strongly and test in succession 
both the inner and the outer 
surface, using a proof plane to 
convey the charge to the electro¬ 
scope. The inner surface will 
give no sign of electrification. 


Hence, it appears that 
the electrical charge of a 
conductor is confined to its 
outer surface. 


Figure 361. — Charge on Outside. 


amount of divergence of the leaves, 
of the conductor in the same way. 
leaves will be produced by the charge from the small 
end and the least from the sides. 


419. Effect of Shape.— 

Charge electrically an insulated 
egg-shaped conductor (Fig. 362). 
Touch the proof plane to the 
large end, and convey the charge 
to the electroscope. Notice the 
Test the side and the small end 
The greatest divergence of the 


The experiment shows that the surface 
density is greatest at the small end of the 
conductor. 

By surface density is meant the quantity 
of electrification on a unit area of the sur¬ 
face of the conductor. 


Figure 362.— 
Surface Density 
Dependent on 
Curvature. 


The distribution of the charge is, therefore, 
affected by the shape of the conductor, the surface density 
being greater the greater the curvature. 








ACTION OF POINTS 


347 


420. Action of Points. — Attach a sharp-pointed rod to one pole of 
an electrical machine (§ 433), and suspend two pith balls from the same 
pole. When the machine is worked there will be little or no separa¬ 
tion of the pith balls. Hold a lighted candle 
near the pointed rod; the candle flame will 
be blown away as by a stiff breeze (Fig. 363). 

The experiment shows that an elec¬ 
tric charge is carried off by pointed 
conductors. This conclusion might 
have been drawn from the preceding 
experiment. When the curvature 
of the egg-shaped conductor becomes 
very great so that the surface be¬ 
comes pointed, the surface density 
also becomes great and there is an intense field of electric 
force in the immediate neighborhood. The air particles 
touching the point become heavily charged and are then 
repelled; other particles take their place and are in turn 
repelled and form an electrical wind. The conductor gives 
up its charge to the repelled particles of air. 

Questions 

1. When a charge is conveyed by a proof plane to an electroscope, 
does the proof plane give up its entire charge ? 

2. Why will not an electroscope remain charged indefinitely? 

3. If the ball of an electroscope were hollow with an aperture so 
that the charged proof plane could be introduced, would any charge 
remain on the proof plane after touching the inside of the ball ? 

4. Will dust have any effect on the working of electrical apparatus ? 

5. Why should electrical apparatus be warmer than the room if 
we are to get good results in electrostatic experiments ? 

6. Why does electrostatic apparatus work better in cold weather 
than in warm ? 

7. Place an electroscope in a cage of fine wire netting. Why is it 
not affected by an electrified glass rod held near it? 



Figure 363. — Flame 
Blown Away by Dis¬ 
charge from Point. 


348 


ELECTROSTATICS 


8. Why does not a metal rod held in the hand and rubbed with 
silk show electrification? 

9. With a positively charged globe, how could another insulated 
globe be charged without reducing the charge on the first one ? 

10. In charging an electroscope by induction, why must the finger 
be withdrawn before removing the inducing charge ? 


IV. ELECTRIC POTENTIAL AND CAPACITY 

421. The Unit of Electrification or Charge. —Imagine two 
minute bodies similarly charged with equal quantities 
of electricity. They will repel each other. If the two 
equal and similar charges are one centimeter apart in air, 
and if they repel each other witli a force of one dyne, 
then the charges are both unity. The electrostatic unit of 
quantity is that quantity which will repel an equal and similar 
quantity at a distance of one centimeter in air with a force of 
one dyne. It is necessary to say “ in air ” because, as will 
be seen later, the force between two charged bodies depends 
on the nature of the medium be¬ 
tween them (§ 427). 

This electrostatic unit is very 
small and has no name. In prac¬ 
tice, a larger unit, called the coulomb , 
is employed. It is equal to 3 x 10 9 
electrostatic units. 

422. Potential Difference. — The 
analogy between pressure in hydro¬ 
statics and potential in electrostatics 
is a very convenient and helpful 
one. Water will flow from the tank 
A to the tank B (Fig. 364) when the stopcock S in the 
connecting pipe is open if the hydrostatic pressure at 
a is greater than at b ; and the flow is attributed directly 
to this difference of pressure. 



Figure 364. — Illustrating 
Potential Difference. 





















ZERO POTENTIAL 


349 



0 


Figure 365. — Conductor A op 
Higher Potential than Conduc¬ 
tor B . 


In the same way, if there is a flow of positive electricity 
from A to B when the two conductors are connected by a 
conducting wire r (Fig. 365), the electrical potential is 
said to be higher at A than 
at B , and the difference of 
electrical potential between 
A and B is assigned as the 
cause of the flow. In both 
cases the flow is in the di¬ 
rection of the difference of 
pressure or difference of potential, irrespective of the fact 
that B may already contain more water because of its 
large cross section, or a greater electric charge because of 
its larger capacity (§ 425). 

If the electric charge in a system of connected conduc¬ 
tors is in a stationary or static condition, there is then 
no potential difference between different points of the 
system. 

The potential difference between two conductors is meas¬ 
ured by the work done in carrying a unit electric charge 
from the one to the other. 

423. Unit Potential Difference. — There is unit potential 
difference between two conductors when one erg of work 
is required to transfer the unit electric charge from one 
conductor to the other. This is called the absolute 
unit; for practical purposes it has been found more con¬ 
venient to employ a unit of potential difference (P. D.), 
which is of the absolute unit, and which is called the 
volt , in honor of the Italian physicist, Alessandro Volta. 

424. Zero Potential. — In measuring the potential differ¬ 
ence between a conductor and the earth, the potential of 
the earth is assumed to be zero. The potential difference 
is then numerically the potential of the conductor . If a 



350 


ELECTEOSTA TICS 


conductor of positive potential be connected with the 
earth by an electric conductor, the positive charge will 
flow to the earth. If the conductor has a negative poten¬ 
tial, the flow of the positive quantity will be in the other 
direction. 

425. Electrostatic Capacity. — If water be poured into a 
cylindrical jar until it is 10 cm. deep, the pressure on the 
bottom of the jar is 10 g. of force per square centimeter. 
If the depth of the water be increased to 20 cm., the pres¬ 
sure will be 20 g. of force per square centimeter (§ 53). 
It thus appears that there is a constant relation between 
the quantity of water Q and the pressure P ; that is, 

= (7, a constant. 

Again, if a gas tank be filled with gas at atmospheric pres¬ 
sure, it will exert a pressure of 1033 g. of force per square 
centimeter (§ 81). If twice as much gas be pumped into the 
tank, the pressure by Boyle’s law (§ 87) will be doubled 
at the same temperature ; that is, there is a constant re¬ 
lation between the quantity of gas Q and the pressure P 

of the gas in the tank, or -^ = (7, a constant as before. 

In the same way, if an electric charge be given to an 
insulated conductor, its potential will be raised above that 
of the earth. If the charge be doubled, the potential 
difference between the conductor and the earth will also 
be doubled. Precisely as in the case of the water and of 
the gas, there is a constant relation between the amount 
of the charge Q and the potential difference V between 

the conductor and the earth ; that is, C. This ratio 

or constant O is the electrostatic capacity of the conductor. 

If V= 1, then C = Q; from which it follows that the 


INFLUENCE OF THE DIELECTRIC 


351 


electrostatic capacity of a conductor is equal to the charge re - 
quired to raise its potential from zero to unity. 

From -2.= C we have Q= CV, and V= Q- (Equation 34) 

426. Condensers. — Support a metal plate in a vertical position 
on an insulating base (Fig. 366). Connect it to the knob of an elec¬ 
troscope by a fine copper wire. Charge the plate until the leaves of 
the electroscope show a wide divergence. Now bring an uninsulated 
conducting plate near the charged one 
and parallel to it. The divergence of 
the leaves will decrease; remove the 
uninsulated plate and the divergence 
will increase again. 

The capacity of an insulated 
conductor is increased by the 
presence of another conductor Figure 366. — Condenser 
connected with the earth. The 

effect of this latter conductor is to decrease the potential 
to which a given charge will raise the insulated one. 
Such an arrangement of parallel conductors separated by 
an insulator or dielectric is called a condenser. 

A condenser is a device which greatly increases the 
charge on a conductor without increasing its potential. In 
other words, the plate connected with the earth greatly 
increases the capacity of the insulated conductor. 

427. Influence of the Dielectric. — Charge the apparatus of the 
last experiment, with the uninsulated plate at a distance of about 
5 cm. from the charged plate and parallel to it, thrust suddenly be¬ 
tween the two a cake of clean paraffin as large as the metal plates or 
larger, and from 2 to 4 cm. thick. Note that the leaf of the electro¬ 
scope (Fig. 356) collapses slightly. Remove the paraffin quickly, and 
the divergence will increase again. A cake of sulphur will produce 
a more marked effect on the divergence of the leaf. 










352 


ELECTROSTATICS 



Figure 367. — Ley¬ 
den Jar. 


The presence of the paraffin or the sulphur increases 
the capacity of the condenser and, hence, decreases its 
potential, the charge remaining the same. 
Paraffin and sulphur, as examples of 
dielectrics, are said to have a larger 
dielectric capacity or dielectric constant 
than air. Glass has a dielectric capacity 
from four to ten times greater than 
air. 

428. The Leyden Jar is a common and 
convenient form of condenser. It con¬ 
sists of a glass jar coated part way up, 
both inside and outside, with tin-foil 
(Fig. 367). Through the wooden or 
ebonite stopper passes a brass rod, ter¬ 
minating on the outside in a ball and on the inside in a 
metallic chain which reaches the bottom of the jar. The 
glass is the dielectric separat¬ 
ing the two tin-foil conduct¬ 
ing surfaces. 

429. Charging and Discharg¬ 
ing a Jar. — To charge a Ley¬ 
den jar connect the outer 
surface to one pole of an 
electrical machine (§ 433), 
either by a metallic conductor 
or by holding the jar in the 
hand. Hold the ball against 
the other pole. To discharge a Leyden jar bend a wire 
into the form of the letter V. With one end of the wire 
touching the outer surface of the jar (Fig. 368), bring the 
other around near the ball, and the discharge will take 
place. 



Figure 368. —Discharging a 
Leyden Jar. 













THEORY OF THE LEYDEN JAR 


353 


430. Seat of Charge. — Charge a Leyden jar made with movable 
metallic coatings (Fig. 369) and set it on an insulating stand. Lift 
out the inner coating, and then, taking the top of the glass vessel in 
one hand, remove the outer coating with the 
other. The coatings now exhibit no sign of 
electrification. Bring the glass vessel near a 
pile of pith balls; they will be attracted to it, 
showing that the glass is electrified. Reach 
over the rim with the thumb and forefinger 
and touch the glass. A slight discharge may 
be heard. Now build up the jar by putting 
the parts together; the jar will still be highly 
electrified and may be discharged in the 
usual way. 

This experiment was devised by 
Franklin ; it seems that electrification Figure 369. Seat 
is a phenomenon of the glass, and that 
the metallic coatings serve merely as conductors, making 
it possible to discharge all parts of the glass at once. 
Some claim that the moisture condensed on the glass acts 
as a conductor when the metallic coatings are removed. 

431. Theory of the Leyden Jar. — A Leyden jar may be 
perforated by overcharging, may be discharged by heat¬ 
ing, and if heavily charged is not completely discharged 
by connecting the two coatings; if left standing a few 
seconds, the two coatings gradually acquire a small 
potential difference and a second small discharge may 
be obtained, known as the residual charge. It appears, 
therefore, that the glass of a charged jar is strained or 
distorted; like a twisted glass fiber, it does not return at 
once to its normal state when released. 

The two surfaces of the glass are oppositely electrified, 
the one charge acting inductively through the glass and 
producing the opposite electrification on the other surface. 
The two charges are held inductively and are said to be 



354 


ELECTROSTATICS 


“ bound,” in distinction from the charge on an insulated 
conductor, which is said to be “free.” 


Questions 


1. Will a charged Leyden jar be discharged by touching the knob 
while the, jar rests on a sheet of hard rubber? 

2. Will a Leyden jar be appreciably charged by applying charges 
to the knob while the jar rests on a sheet of hard rubber? 

3 . In discharging a Leyden jar with a bent wire, why not touch 
the wire to the knob before touching the outside surface ? 

4 . Cuneus tried to charge a bowl of water by holding it in his 
hand, while the chain of an electrical machine dipped into the water. 
When he lifted the chain with the other hand he got a shock. Why? 

5 . Explain why a small metal ball suspended by a silk thread 
between two bodies, the two being near together and charged, one 
negatively and the other positively, flies back and forth between the 
two bodies. 


V. ELECTRICAL MACHINES 


432. The Electrophorus. — The simplest induction elec¬ 
trical machine is the electrophorus (Fig. 370), invented by 


Volta. A cake of resin or 
disk of vulcanite A rests in 
a metallic base B. Another 
metallic disk or cover C is 
provided with an insulating 
handle D. The resin or vul¬ 
canite is electrified by rub¬ 
bing with dry flannel or 
striking with a catskin, and 
the metal disk is then placed 



Figure 370. — Electrophorus. .. ~ r 

on it. since the cover 

touches the nonconducting resin or vulcanite A in a few 
points only, the negative charge due to the friction is 
not removed. The two disks with the film of air be¬ 
tween them form a condenser (§ 426) of great capacity. 



INFLUENCE ELECTRICAL MACHINES 


355 


Touch the cover momentarily with the finger, and the repelled 
negative charge passes to the earth, leaving the cover at zero poten¬ 
tial. Lift it by the insulating handle, the positive charge becomes 
free (§ 431), and a spark may be drawn by holding the finger near it. 
This operation may be repeated an indefinite number of times with¬ 
out sensibly reducing the charge on the vulcanite. 

When the cover is lifted by the insulating handle, work 
is done against the electrical attraction between the nega¬ 
tive charge on the vulcanite and the positive on the cover. 
The energy of the charged cover represents this work. 

The electrophorus is, therefore, a device for transforming 
energy in some other form into the energy of electric charges. 

433. Influence Electrical Machines. — There are many in¬ 
fluence or induction electrical machines, but it will suffice 
to describe only one, as the principle is always the same. 



Figure 371. — Toepler-Holtz Machine. 


The Holtz machine, as modified by Toepler and Voss, 
is illustrated in Fig. 371. There are two glass plates, e f 
and e , about 5 mm. apart, the former stationary and the 



























356 


ELECTROSTA TICS 


latter turning about an insulated axle by means of the 
crank h and a belt. The stationary plate supports at the 
back two paper sectors, c and c\ called armatures. Be¬ 
tween them and the stationary plate e l are disks of tin-foil 
connected by a narrow strip of the same material. The 
disks are electrically connected with two bent metal arms, 
a and a r (opposite a), which carry at the other end tin¬ 
sel brushes long enough to rub against low brass buttons 
cemented to small tin-foil disks, called carriers , on the 
front of the revolving plate. Opposite the paper sectors 
and facing them are two metal rods with several sharp- 
pointed teeth set close to the revolving plate, but not 
touching the metal buttons and carriers. The diagonal 
neutralizing rod d has tinsel brushes in addition to the 
sharp points. The two insulated conductors, terminating 
in the balls, m and w, have their capacity increased by con¬ 
nection with the inner coating of 
two small Leyden jars, i and i '; 
the outer coatings are connected 
under the base of the machine. 

There are so many varieties of 
induction machines, and the ex¬ 
planation of their operation is so 
involved and uncertain, that we 
shall leave it for those interested 
in the subject to look it up in 
special books on electricity. 

434. Experiments with Electrical 
Machines. — 1. Attraction and repulsion. 
Place a number of bits of paper on the 
cover of a charged electrophorus. Lift it by the insulating handle. 
The charged pieces of paper fly off 1 he plate. 

Three bells are suspended from a metal bar (Fig. 372). The 



Figure 372. — Bells Rung 
by Electrification. 








EXPERIMENTS WITH ELECTRICAL MACHINES 357 



Figure 373. — Electri¬ 
cal Tourniquet. 


middle one is insulated from the bar; the others are suspended by 
chains. Connect the bar to one pole of an electrical machine and the 
middle bell to the other. The small brass balls between the bells are 
suspended by silk cords; they swing to and 
fro between the bells, carrying positive charges 
in one direction and negative in the other. 

This apparatus, called the electrical chimes, 
is of interest because it was employed by 
Franklin in his lightning experiments to an¬ 
nounce the electrification of the cord leading 
to the kite (§ 435). 

2. Discharge by points. Connect an electri¬ 
cal tourniquet (Fig. 373) to one of the con¬ 
ductors of an electrical machine, the other con¬ 
ductor being grounded. When the machine 
is turned, the whirl rotates rapidly (§ 420). 

3. Mechanical effects. Hold a piece of cardboard between the dis¬ 
charge balls of an electrical machine. It will be perforated by a 
spark and the holes will be burred out on both sides. A thin dry 
glass plate, or a thin test tube over a sharp point, may be perforated 
by a heavy discharge. 

4. Heating effects. Charge a Leyden jar and connect its outer coat¬ 
ing with a gas burner by a chain or wire. Turn on the gas and bring 
the ball of the jar near enough to the opening in the burner to allow 

a spark to pass. The gas will be lighted 
by the discharge. 

Fill a gas pistol with a mixture of coal 
gas and air. Discharge a Leyden jar 
through the mixture. It will explode 
and the cork or ball will be shot out with 
some violence. 

Magnetic effects. Wind insulated cop¬ 
per wire around a small glass tube (Fig. 
374), and place inside the tube a piece 
of darning needle. Discharge a Leyden 
jar through the wire. The needle will 
be magnetized. A similar effect may be 
produced by placing a large sewing needle across a strip of tin-foil 
forming a part of the discharge circuit of a Leyden jar. 



Figure 374. — Needle 
Magnetized by Electric Dis¬ 
charge. 


















358 


ELECTROSTATICS 


VI. ATMOSPHERIC ELECTRICITY 

435. Lightning. — Franklin demonstrated in 1752 that 
lightning is identical with the electric spark. He sent up 
a kite during a passing storm, and found that as soon as 
the hempen string became wet, long sparks could be drawn 

from a key attached to 
it, Leyden jars could be 
charged, and other effects 
characteristic of static 
electrification could be 
produced. The string 
was not held in the hand 
directly, but by a silk 
ribbon tied to it for 
safety. 

Lightning flashes are 
discharges between op¬ 
positely charged bodies. 
They occur either be¬ 
tween two clouds or 
between a cloud and the 
earth (Fig 375). The 
rise of potential in a cloud causes a charge to accumulate 
on the earth beneath it. If the stress in the air reaches a 
value of about 400 dynes per square centimeter, the air 
breaks down, or is ruptured, like any other dielectric, and 
the two opposite charges unite in a long zigzag flash. A 
lightning flash allows the strained medium to return to 
equilibrium. The coming together of the air surfaces, 
which are separated in the rupture, produces a violent 
crash of thmider. If the path of the flash be long and 
zigzag, the observer will hear successive sounds from differ- 



Figure 375. — Lightning Discharge. 




Benjamin Franklin (1706-1790) was born at Boston, Massa¬ 
chusetts. In his twentieth year he was apprenticed to his elder 
brother in the printing business. When forty years of age he saw 
some electrical experiments performed with a glass tube. These 
excited his curiosity and he began experimenting for himself. In 
less than a year he had discovered the discharging effects of points 
and worked out a theory of electricity, known as the “ one-fluid 
theory.” He explained the charged Leyden jar, established the 
identity of lightning and the electric spark, invented an electric 
machine, and introduced the lightning rod as a protection against 
lightning. He was distinguished as a statesman, diplomatist, and 
scientist. He founded the American Philosophical Society and 
the University of Pennsylvania. 










THE LIGHTNING ROD 


359 


ent parts of the path as a crackling rattle ; then the echoes 
from other clouds will come rolling in afterwards. The 
duration of a lightning flash is never more than 
of a second. If it lasted much longer, its intensity is so 
great that it would be blinding. 

436. The Lightning Rod. — Support two round metal plates, 
T and T', one above the other and a few centimeters apart (Fig. 
376). The upper plate 

must be carefully insulated || B | 

except from the pole of the 
electrical machine and the 
inner coating of a Leyden 
jar L. Two of the short 
rods on the lower plate 
terminate in small balls; 
the other and shortest one 
is pointed. When the ma¬ 
chine is worked, the ten¬ 
sion between the plates 
increases, but it is difficult to make a spark pass; if one does pass, it 
will strike the pointed rod. 

The experiment illustrates the protection afforded by a 
pointed conductor. 

A lightning rod should conform to the following 
requirements: 

First. It should be perfectly continuous, of sufficient 
size to resist fusion, and made preferably of strands of 
wire twisted together as a cable. Iron cables are as good 
as copper ones. 

Second. The upper end should terminate in points and 
should be higher than adjacent parts of the building. 
The lower end should pass down into the earth until it 
enters a moist conducting stratum. 

Third. The rod should be fastened to the building 
without insulators, and all metal parts of the roof should 






T 


Figure 376. — Protection by Pointed 
Rod. 



















360 


ELECTROSTATICS 


be connected with the main conductor. It is better to 
have two or three descending rods than one, and all the 
points and rods should be connected together as a network. 

The protection afforded by lightning rods, properly 
erected, is abundantly proven by the statistics of mutual 
fire insurance companies for buildings in the country. 

437. Oscillatory Discharge. — When a Leyden jar is highly 

charged, the potential difference between its coatings increases until 
the dielectric between the discharge terminals suddenly breaks down 
and a spark passes. This discharge usually consists of several oscilla¬ 
tions or to-and-fro discharges, like the vibrations of an elastic system 
or the surges of a mass of water after sudden release from pressure. 
Imagine a tank with a partition across the middle and filled on one 
side with water. If a small hole be made in the partition near the 
bottom, the water will slowly reach the same level on both sides with¬ 
out agitation; but if the partition be suddenly removed, the first 
violent subsidence will be succeeded by a return surge, and the to-and- 
fro motion of the water will continue with decreasing violence until 
the energy is all expended. 

A series of similar surges occurs when a condenser is suddenly dis¬ 
charged by the breaking down of the dielectric. The oscillatory char¬ 
acter of such electric discharges was discovered by Joseph Henry in 
1842. Its importance has been recognized only in recent times. Simi¬ 
lar electric oscillations probably take place in some lightning flashes. 

438. The Aurora. — The aurora is due to silent discharges 
in the upper regions of the atmosphere. Within the arctic 
circle it occurs almost nightly, and sometimes with in¬ 
describable splendor. The illumination of the aurora is 
due to positive discharges passing from the higher regions 
of the atmosphere to the earth. In our latitude these 
silent streamers in the atmosphere are infrequent. When 
they do occur they are accompanied by great disturbances 
of the earth’s magnetism and by earth currents. Such 
magnetic disturbances sometimes occur at the same time 
in widely separated portions of the earth. 


CHAPTER XII 


ELECTRIC CURRENTS 
I. VOLTAIC CELLS 

439. An Electric Current. — The discharge of a condenser 
through a wire produces in and around the wire a state 
called an electric current. If by any arrangement elec¬ 
tricity could be supplied to the condenser as fast as it is 
conveyed away through the wire, a continuous current 
would be produced. Any arrangement by which the ends 
of a conducting wire are kept at different potentials will 
insure the flow of a continuous current through it. 

It is analogous to the flow of heat through a metal rod 
if one end is kept at a higher temperature than the other, 
the heat flowing from the hotter to the colder end. So also 
a stream of water flows through a section of pipe if the 
pressure at one end is maintained higher than at the other. 
It is customary to consider the electric current as flowing 
from positive to negative, that is, from higher potential 
to lower. 

One of the simplest means of maintaining a potential 
difference between the terminals of a conductor is the 
primary or voltaic cell. 

440. The Voltaic Cell. — Support a heavy strip of zinc and one 
of sheet copper (Fig. 377) in dilute sulphuric acid (one part acid to 
twenty of water). After the zinc has been in the acid a short time, 
it should be amalgamated by rubbing it with mercury. There will be 
no apparent change when the plates are replaced in the acid, until 

301 


362 


ELECTRIC CURRENTS 


the two are connected with a copper wire; a multitude of bubbles of 
hydrogen gas will then immediately be given off at the surface of the 
copper plate. The action ceases as soon as the wires are discon¬ 
nected. If the action is continued for some 
time, the zinc will waste away, while the 
copper is not affected. 

Such a combination of two con¬ 
ductors, immersed in a compound 
liquid, called an electrolyte , which is 
capable of reacting chemically with 
one of the conductors, is called a 
voltaic cell. The name is derived 
from Volta of Padua, who first de¬ 
in 1800. 

441. Plates Electrically Charged. — In a condensing electro¬ 
scope the ball at the top is replaced by a brass disk coated with thin 
shellac varnish as an insulator. Resting on 
it is a second disk to which is fitted an insu¬ 
lating handle. The two disks with the shellac 
varnish between them form a condenser of 
considerable capacity. 

Connect the wire leading from the copper 
plate of two or three voltaic cells C in series 
(§ 473) to the lower disk A of the electro¬ 
scope, and the wire from the zinc plate to the 
upper disk B (Fig. 378). Disconnect the wires, 
handling them one at a time by means of a 
good insulator so as not to discharge the con¬ 
denser, and then lift the top disk. The leaf 
L of the electroscope will diverge, and a test 
with an electrified glass rod will show that the 
electroscope is charged positively. This posi¬ 
tive charge was derived from the copper strip 
of the cell. Repeat the experiment with the zinc plate connected 
to the lower disk; the result will be a negative charge on the gold 
leaf. 



of a Voltaic Cell 
Charged. 



Figure 377. — Voltaic 
Cell. 

scribed such a cell 


















ELECTROCHEMICAL ACTIONS IN VOLTAIC CELL 363 


It is clear from this experiment that the plates of a vol¬ 
taic cell and the wires leading from them are electrically 
charged, the copper positively and the zinc negatively. The 
conducting rods, plates, or cylinders in a voltaic cell are 
called electrodes , the copper the positive electrode and the 
zinc the negative electrode. The electric current leaves 
the electrolyte by the positive electrode and enters it by 
the negative. 

442. The Circuit. — The circuit of a voltaic cell com¬ 
prises the entire path traversed by the current, including 
the electrodes and the liquid in the cell as well as the ex¬ 
ternal conductor. Closing the circuit means joining the 
two electrodes by a conductor ; breaking or opening the cir¬ 
cuit is disconnecting them. So when the circuit is broken 
at any point by a key, a switch, or a push button, the cir¬ 
cuit is said to be open; when the key or switch is closed, 
so as to make a continuous path for the current, the circuit 
is said to be closed. The flow of current in the external 
circuit is from the positive electrode (copper) to the 
negative (zinc), and in the internal part of the circuit 
from the negative electrode to the positive (Fig. 377). 

443. Electrochemical Actions in a Voltaic Cell. — The 
theory of dissociation furnishes an explanation of the 
manner in which an electric current is conducted through 
a liquid. It is briefly as follows : When a chemical com¬ 
pound such as sulphuric acid (H 2 S0 4 ),* for example, is 
dissolved in water, some of the molecules at least split into 
two parts (H 2 and S0 4 ), one part having a positive elec¬ 
trical charge and the other a negative one. 

The two parts of the dissociated substance with their 


* Each molecule of sulphuric acid is composed of two atoms of hydrogen 
(Ha), one of sulphur (S), and four of oxygen (0 4 )- 



364 


ELECTRIC CURRENTS 


electrical charges are called ions (from a Greek word 
meaning to go). An electrolyte is a compound capable of 
such dissociation into ions. It conducts electricity only 
by means of the migration of the ions resulting from the 
splitting in two of the molecules. The separated ions 
convey their charges with a slow and measurable velocity 
through the liquid. Electropositive ions, such as zinc and 
hydrogen, carry positive charges in one direction, electro¬ 
negative ions, such as “ sulphion ” (S0 4 ), carry negative 
charges in the opposite direction, 
and the sum of the two kinds of 
charges carried through the liquid 
per second is the measure of the 
current. 

Figure 379 represents a sec¬ 
tion of a voltaic cell with the 
electropositive and electroneg¬ 
ative ions. When the cir- 


-> 



Figure 379 —Section of Cell cuit is closed and a current 
with Ions. flows, zinc from the zinc plate 

++ 

enters the solution as electropositive ions (Zn), while the 
positive hydrogen ions migrate toward the copper plate or 
cathode, and the sulphions toward the zinc plate. The 


S0 4 ions carry negative charges to the zinc plate, so that 
it becomes charged negatively, while the H 2 ions carry 
positive charges to the copper plate and it becomes 
charged positively. Zinc from the zinc plate thus goes 
into solution as zinc sulphate (ZnS0 4 ), and hydrogen 
when it has given up its positive charge is set free as 
gaseous hydrogen on the copper plate. Some prefer to 
say that when the zinc ions with their positive charge 
leave the zinc plate, the equivalent negative is left behind 











DIFFERENCE OF POTENTIAL 


365 


to charge the zinc electrode. The zinc ions unite with 
the sulphions to form neutral zinc sulphate. Thus, while 
the zinc ions are electropositive and carry positive charges, 
the zinc plate is charged negatively. 

444. Electromotive Force. — Imagine a rotary pump 
which produces a difference of pressure between its inlet 
and its outlet. Such a pump may cause water to circulate 
through a system of horizontal pipes against friction. In 
any portion of the pipe system the force producing the 
flow is the difference of water pressure between the ends 
of that portion. But the force is all applied at the pump, 
and this produces a pressure throughout the whole circuit. 
A voltaic cell is an electric generator analogous to such a 
pump. 

A voltaic cell generates electric pressure called electro¬ 
motive force . It does not generate electricity any more 
than the pump generates water, but it sup- 
plies the electric pressure to set electricity 
flowing. This electromotive force (E.M.F.) 
is numerically equal to the work which must 
be done to transport a unit quantity of elec¬ 
tricity around the external circuit from A to 
B , through the zinc plate to Z, from Z 
through the liquid (7, and thence back to A 
(Fig. 380). Work is done in this transfer, 
because all conductors offer resistance to the 
passage of a current. The energy thus ex¬ 
pended goes to heat the conductor. A vol¬ 
taic cell is thus a device for transforming chemical energy 
into the energy of an electric current. 

445. Difference of Potential. — The difference of poten¬ 
tial between two points, A and B , on the external conduct¬ 
ing circuit is the work done in carrying a unit quantity of 


A 


B 


if 



mui 


b 

====== 

u 


Figure 380. 
— Circuit 
through Vol¬ 
taic Cell. 












366 


ELECTRIC CURRENTS 


electricity from the one point to the other. The difference 
of potential between the electrodes of a voltaic cell when 
the circuit is closed is less than the E.M.F. of the cell by 
the work done in transferring unit quantity of electricity 
through the electrolyte. If E denotes this potential dif¬ 
ference and Q the quantity conveyed, then the whole work 
done is the product EQ. But the quantity conveyed by 
a conductor per second is called the strength of current , I. 
The energy transformed in a conductor, therefore, when 
current I flows through it, under an electric pressure or 
potential difference of E units between its ends, is El ergs 
per second. 

446. Detection of Current. — Solder a copper wire to each of 
the strips of a voltaic cell, and connect the wires with some form of 


key to close the circuit. 
Stretch a portion of the 
wire over a mounted 
magnetic needle (Fig. 
381), holding it paral¬ 
lel to it and as near as 
possible without touch¬ 
ing. Now close the 



+ 


Figure 381. — Deflection of Needle by Current, circuit; the needle is 

deflected, and comes to 

rest at an angle with the wire. Next form a rectangular loop of the 
wire, and place the needle within it. A greater deflection is now ob¬ 
tained. If a loop of several turns is formed, the deflection is still 
greater. 

A magnetic needle employed in this way becomes a 
galvanoscope , a detector of electric currents. This experi¬ 
ment, first performed by Oersted in 1819, shows that the 
region around the wire has magnetic properties during the 
flow of electricity through the wire. In other words, it is 
a magnetic field (§ 398), 







Hans Christian Oersted (1777-1851) was born at Rudkjo- 
bing, Denmark, and received his education at the University of 
Copenhagen, afterward becoming professor in the University and 
polytechnic school of that city. It was while holding this posi¬ 
tion that he discovered the action of the electric current on the 
magnetic needle, thus establishing the connection between elec¬ 
tricity and magnetism which had long been sought by scientists. 
He also discovered that this magnetic action of the electric cur¬ 
rent takes place freely through a great many substances. Oersted 
wrote extensively for newspapers and magazines in an endeavor 
to make science popular. 






























































■ ■ i 









I* 








•« *1 

«- 
























' . 








. * ’ . 





























- * 


• .. . 






- ' .. 






- 






f 























* • •• <• 
























LOCAL ACTION 


367 


447. Relation between the Direction of the Current and the 
Direction of Deflection. — Making use of the apparatus of § 446, 
compare the direction of the current through the wire with that in 
which the north pole of the needle turns. Cause the current to pass 
in the reverse direction over the needle; the deflection is reversed. 
Now hold the wire below the needle, and the direction of deflection is 
again reversed as compared with the deflection when the wire is held 
above the magnetic needle. 

The direction of the deflection may always be predicted 
by the following rule : Stretch out the right hand along the 
wire , with the palm turned 
toward the magnetic needle , 
and with the current flowing 
in the direction of the ex¬ 
tended fingers. The out¬ 
stretched thumb will then 
point in the direction in 
which the north pole of the needle is deflected (Fig. 382). 
By the converse of this rule, the direction of the current 
may be inferred from the direction in which the needle 
is deflected. 

448. Local Action. — Place a strip of commercial zinc in dilute 
sulphuric acid. Hydrogen is liberated during the chemical action, 
and after a few minutes the zinc becomes black from particles of car¬ 
bon exposed to view by dissolving away the surface. If the experi¬ 
ment is repeated with zinc amalgamated with mercury, that is, by 
coating it with an alloy of mercury and zinc, there will be little or no 
chemical action. A strip of chemically pure zinc acts much like one 
amalgamated with mercury. 

Thus we see that the amalgamation of commercial zinc 
with mercury changes its properties. If in the experiment 
with the simple voltaic cell, a galvanoscope is inserted in 
the circuit both before the zinc has been amalgamated and 



Figure 382.—Direction of Deflection. 




368 


ELECTRIC CURRENTS 


afterward, it will be found that a larger deflection will be 
obtained in the second case. 

In a voltaic cell the chemical action which contributes 
nothing to the current flowing through the circuit is 
known as local action . It is probably due to the presence 
of carbon, iron, etc., in the zinc ; these with the zinc form 
miniature voltaic cells, the currents flowing around in short 
circuits from the zinc through the liquid to the foreign 
particles and back to the zinc again. 

This local action is prevented by amalgamating the zinc. 
The amalgam brings pure zinc to the surface, covers the 
foreign particles, and above all forms a smooth surface, so 
that a film of hydrogen clings to it and protects it from 
chemical action save when the circuit is closed. 

449. Polarization. — Connect the poles of a voltaic cell to a gal* 
vanoscope and note the deflection. Let the cell remain in circuit with 
the galvanoscope for some time; the deflection 
will gradually become less and less. Now stir 
up the liquid vigorously with a glass rod, in¬ 
serting the rod between the plates and brush¬ 
ing off the adhering gas bubbles \ the deflec¬ 
tion will increase nearly to its first value. 

Fasten two strips of zinc and two of copper 
to a square board and immerse them in dilute 
sulphuric acid (Fig. 383). Join one zinc and 
one copper strip with a short wire for a few 
minutes. Then disconnect and join the two 
coppers to a galvanoscppe. The direction of 
the deflection will be the same as if zinc were 
used in place of the copper strip coated with 
hydrogen. The hydrogen-coated copper acts like zinc and tends to 
produce a current through the electrolyte from it to the copper free 
from hydrogen. 

The diminution in the intensity of the current is due to 
several causes, but the chief one is the film of hydrogen 



Figure 383. — To Show 
Polarization. 








REMEDIES FOR POLARIZATION 


369 


which gathers on the copper plate, causing what is known 
as the polarization of the cell. The hydrogen on the posi¬ 
tive plate not only introduces more resistance to the flow of 
the current, but it diminishes the electromotive force to 
which this flow is due. The presence of hydrogen on 
the copper plate sets up an inverse E.M.F., which reduces 
the flow. 

450. Remedies for Polarization. — Place enough pure mercury 
in a quart jar to cover the bottom, and hang above it a piece of sheet 
zinc. Fill the jar with a nearly saturated solution of salt water, and 
place in the mercury the exposed end of a copper wire insulated with 
gutta-percha, the mercury forming the positive electrode of the bat¬ 
tery. 

If now the circuit is closed through a telegraph sounder (§ 552) of 
ten or fifteen ohms resistance, the armature will at first be attracted 
strongly; but in the course of a few minutes it will be released and 
will be drawn back by the spring. Polarization has then set in to the 
extent that the current is insufficient to operate the instrument. 

Next take a small piece of mercuric chloride (HgCl 2 ) no larger 
than the head of a pin, and drop it in on the surface of the mercury. 
The armature of the sounder will instantly be drawn down, showing 
that the current has recovered its normal value. The hydrogen has 
been removed by the chlorine of the mercuric chloride. In a few 
minutes the chlorine will be exhausted, and polarization will again 
set in. A little more of the chloride will again restore the activity of 
the cell. (This experiment was devised several years ago by Mr. D. 
H. Fitch.) 

This illustrates a chemical method of reducing polariza¬ 
tion. The hydrogen ions are replaced by others, such as 
copper or mercury, which do not produce polarization 
when they are deposited on the positive electrode; or else 
the positive electrode is surrounded with a chemical which 
furnishes oxygen or chlorine to unite with the hydrogen 
before it reaches the electrode. In both cases the elec¬ 
trode is kept nearly free from hydrogen. 


870 


ELECTRIC CURRENTS 


451. The Daniell Cell. — The Daniell cell in its most 
common form (Fig. 384) consists of a glass jar containing 

a saturated solution of copper sul¬ 
phate (CuS0 4 ), and in it a cylinder 
0 of copper, which is cleft down one 
side. Within the copper cylinder is 
a porous cup of unglazed earthenware 
containing a dilute solution of zinc 
sulphate (ZnS0 4 ). In the porous 
cup also is the zinc prism Z. The 
copper sulphate must not be allowed 
to come in contact with the zinc elec¬ 
trode. The porous cup allows the 
ions to pass through its pores, but it 
prevents the rapid admixture of the 
two sulphates. 

Both electrolytes undergo partial dissociation into ions; 
and when the circuit is closed, the zinc and the copper 
ions both travel toward the copper electrode. The zinc 
ions do not reach the copper, because zinc in copper sul¬ 
phate replaces copper, forming zinc sulphate. The result 
is the formation of zinc sulphate at the zinc electrode and 
the deposition of metallic copper on the copper electrode. 
Polarization is completely obviated; and, so long as the 
circuit is kept closed, the mixing of the electrolytes by 
diffusion is slight. This cell must not be left on open 
circuit because the copper sulphate then diffuses until it 
reaches the zinc and causes a black deposit of copper oxide 
on it. 

452. The Gravity Cell. — This cell (Fig. 385) is a modi¬ 
fied Daniell. The porous cup is omitted, and the partial 
separation of the liquids is secured by difference in density. 
The copper electrode Q is placed at the bottom in saturated 



Figure 384. — Daniell 
Cell. 



THE DRY CELL 


371 


copper sulphate B , while the zinc Z is suspended near the 
top in a weak solution of zinc sulphate A, floating on top 
of the copper sulphate. The zinc 
should never be placed in the solution 
of copper sulphate. The saturated 
copper sulphate is more dense than 
the dilute zinc salt, and so remains 
at the bottom, except as it slowly dif¬ 
fuses upward. 

453. The Leclanche Cell consists of a 
glass vessel containing a saturated 
solution of ammonium chloride (sal 
ammoniac) in which stands a zinc Figure385.— The Grav- 
rod and a porous cup (Fig. 386). 

In this porous cup is a bar of carbon very tightly packed 
in a mixture of manganese dioxide and graphite, or granu¬ 
lated carbon. 

The zinc is acted on by the chlorine of the ammonium 
chloride, liberating ammonia and hydrogen. The am¬ 
monia in part dissolves in the liquid, 
and in part escapes into the air. The 
hydrogen is slowly oxidized by the 
manganese dioxide. The cell is not 
adapted to continuous use, as the hy¬ 
drogen is liberated at the positive 
electrode faster than the oxidation 
goes on, and hence the cell polarizes. 
If, however, it is allowed to rest, it re¬ 
covers from polarization. The Le¬ 
clanche cell is suitable for ringing 
electric bells. 

454. The Dry Cell. — The “ dry ” cell is merely a modi¬ 
fied Leclanche specially adapted for use in situations 



Figure 386.—The Le¬ 
clanche Cell. 


































372 


ELECTRIC CURRENTS 


where cells with a liquid electrolyte cannot be used. 
The electrodes are zinc and carbon. The cylindrical zinc 
pot Z (Fig. 387) is contained in a cardboard case. It is 
lined with porous pulp board, which serves the double 
purpose of taking up part of the liquid content of the cell 
and separating the solid part from 
the zinc. The carbon is either 
round or flat (shown edgeways in 
the figure). Between the two 
electrodes is a moist paste or 
“ mix ” of varied composition, but 
containing the essential sal am¬ 
moniac, besides granulated car¬ 
bon, graphite, zinc chloride, and 
manganese dioxide. The cell is 
sealed with wax or pitch. 

Dry cells of the standard size, 
2| x 6 inches, are now made that 
yield a current of 25 to 30 am¬ 
peres (§ 469) on short circuit. 
Smaller sizes in great numbers are 
used to light miniature electric lights in hand lamps or 
flash lights. Some fifty millions of “ standard ” dry cells 
are now manufactured yearly in the United States, and 
probably several times that number of small cells for hand 
lamps. In addition to their application in flash lights, 
dry cells are much used for ringing bells, running clocks, 
and working spark coils for ignition in gas engines on 
boats and automobiles. It should not be forgotten that 
dry cells must not be left on closed circuit. 

455. The Lalande Cell. — The negative is zinc and the 
exciting liquid is a 30 per cent solution of caustic potash. 
The zinc dissolves in the alkali, forming zincate of potas- 



Figure 387. — Dry Cell. 











ELECTROLYSIS OF COPPER SULPHATE 


373 


sium and setting free hydrogen. The positive electrode 
is a compressed cake of copper oxide, held in a copper 
frame. The hydrogen reduces the copper oxide to me¬ 
tallic copper. The exciting liquid must be covered with 
oil to exclude the carbonic acid gas of the air, which 
converts the alkali into a carbonate. This cell has an 
electromotive force but little more than half that of the 
Leclanchd, but it is capable of furnishing a large and 
constant current. On this account it is much used to 
work railway signals. 

II. ELECTROLYSIS 

456. Phenomena of Electrolysis. — Thrust platinum wires 

through the corks closing the ends of a V-tube (Fig. 388). Fill the 
tube nearly full with a solution of 
sodium sulphate colored with blue 
litmus. Pass through it a current for 
a few minutes. The liquid around 
the anode , where the current enters, 
will turn red, showing the formation 
of an acid; the liquid around the 
cathode , where the current leaves the 
cell, will turn a darker blue, showing Figure 388. — V-Tube for 
the presence of an alkali. Electrolysis. 

The electric current in its passage through a liquid 
decomposes it. This process of decomposing a liquid by 
an electric current Faraday named electrolysis; the liquid 
decomposed he called the electrolyte; the parts of the 
separated electrolyte, ions. The current enters the elec¬ 
trolyte by the anode (meaning the way in ) and leaves it by 
the cathode (meaning the way out). 

457. Electrolysis of Copper Sulphate. — Fill the V-tube of the 
last experiment about two-thirds full of a solution of copper sulphate. 
After the circuit has been closed a few minutes, the cathode will be 




374 


ELECTRIC CURRENTS 


covered with a deposit of copper, and bubbles of gas will rise from 
the anode. These bubbles are oxygen. 

When copper sulphate is dissolved in water it is dis¬ 
sociated to some extent. If, therefore, electric pressure 
is applied to the solution through the electrodes, the 
• ++ 

electropositive ions (Cu) are set moving from higher to 

lower potential, while the electronegative ions (SC> 4 ) carry 

+4- 

their negative charges in the opposite direction. The Cu 
ions are therefore driven against the cathode, and, giving 
up their charges, become metallic copper. The sulphions 
(S0 4 ) go to the anode; and, giving up their charges, 
they take hydrogen from the water 
present, forming sulphuric acid 
(H 2 S0 4 ) and setting free oxygen, 
which comes off as bubbles of gas. If 
the anode were copper instead of plati¬ 
num, the sulphion would unite with it, 
forming copper sulphate, and copper 
would be removed from the anode as 
fast as it is deposited on the 'cathode. 
The result of the passage of a current 
would then be the transfer of copper 
from the anode to the cathode. This 
is what takes place in the electrolytic 
refining of copper. 

Thus the passage of an electric cur¬ 
rent through an electrolyte is accom¬ 
plished in the same way, whether it is 
in a voltaic cell or in an electrolytic 
cell. 

458. Electrolysis of Water. —Water appears to have been 
the first substance decomposed by an electric current. Pure 








LAWS OF ELECTROLYSIS 


875 


water does not conduct an appreciable current of elec¬ 
tricity, but if it is acidulated with a small quantity of 
sulphuric acid, electrolysis takes place. 

In Hofmann’s apparatus (Fig. 389) the acidulated water is poured 
into the bulb at the top, and the air escapes by the glass taps until 
the tubes are filled. The electrodes at the bottom in the liquid are 
platinum foil. If a current is sent through the liquid, bubbles of gas 
will be libera ted on the pieces of platinum foil. The gases collecting 
in the tubes may be examined by letting them escape through the 
taps. Oxygen will be found at the anode and hydrogen at the 
cathode; the volume of the hydrogen will be nearly twice that of the 
oxygen. 

459. Laws of Electrolysis. —The following laws of elec¬ 
trolysis were established by Faraday. 

I. The mass of an electrolyte decomposed by an electric 
current is proportional to the quantity of electricity con¬ 
veyed through it. 

The mass of an ion liberated in one second is, therefore, 
proportional to the strength of current. 

II. When the same quantity of electricity is conveyed 
through different electrolytes, the masses of the different 
ions set free at the electrodes are proportional to their 
chemical equivalents. 

By “ chemical equivalents ” are meant the relative 
quantities of the ions which are chemically equivalent to 
one another, or take part in equivalent chemical reactions. 
Thus, 82.5 g. of zinc or 31.7 g. of copper take the place of 
one g. of hydrogen in sulphuric acid (H 2 S0 4 ) to form zinc 
sulphate (ZnS0 4 ) or copper sulphate (CuS0 4 ), respec¬ 
tively. 

The first law of electrolysis affords a valuable means of 
comparing the strength of two electric currents by deter- 


376 


ELECTRIC CURRENTS 


mining the relative masses of any ion, such as silver or 
copper, deposited by the two currents in succession in the 
same time (§ 469). 

460. Electroplating consists in covering bodies with a 
coating of any metal by means of the electric current. 
The process may be summarized as follows: Thoroughly 
clean the surface to remove all fatty matter. Attach the 
article to the negative electrode of a battery, and sus¬ 
pend it in a solution of some chemical salt of the metal 
to be deposited. If silver, cyanide of silver dissolved 
in cyanide of potassium is used; if copper, sulphate of 
copper. To maintain the strength of the solution a piece 
of the metal of the kind to be deposited is attached 
to the positive electrode of the battery and immersed in 
the electrolyte. The action is similar to that heretofore 
given. Articles of iron, steel, zinc, tin, and lead cannot 
be silvered or gilded unless first covered with a thin coat¬ 
ing of copper. 

All silver plating, nickeling, gold plating, and so on, is 
done by this process. 

461. Electrotyping consists in copying medals, wood-cuts, 
type, and the like in metal, usually copper, by means of the 
electric current. A mold of the object is taken in wax or 
plaster of Paris. This is evenly covered with powdered 
graphite to make the surface a conductor, and treated very 
much as an object to be plated. When the deposit has be¬ 
come sufficiently thick it is removed from the mold and 
backed or filled with type-metal. 

Nearly all books nowadays are printed from electrotype 
plates, and not as formerly from movable types. 

462. The Storage Cell. — Attach two lead plates, to which are 
soldered copper wires, to the opposite sides of a block of dry wood, 
and immerse them in dilute sulphuric acid, one part acid to five of 


THE STORAGE (JELL 


377 



water (Fig. 390) . Connect this cell to a suitable battery B by means 
of key K x ; also to an ordinary electric house bell H through a key K 2 
(Fig. 391). A galvanoscope G may be included in the circuit to show 
the direction of the current. Pass a cur¬ 
rent through the lead cell for a few min¬ 
utes by closing the key K v Hydrogen 
bubbles will be disengaged from the 
cathode, while the anode will begin to 
turn dark brown. Next open the key 
K v thus disconnecting the battery B , and 
close key K 2 . The bell will ring and the 
galvanoscope will indicate a discharge 
current in the opposite direction to the 
first or charging current. The bell will 
soon cease ringing, and the charging may 

be repeated by again closing key K, while 
~ . Figure 390. —Simple Stor- 

An is open. ^ 

2 r age Cell. 


a 


if 

i 


The lead plates in an electrolyte of sulphuric acids il¬ 
lustrate a simple lead storage cell. The electrolysis of the 
sulphuric acid liberates oxygen at the anode, which com¬ 
bines with the lead electrode to form a chocolate-colored 
deposit of lead peroxide (Pb0 2 ). Hydrogen accumulates 

on the cathode. When the 
charging battery is discon¬ 
nected and the lead plates are 
joined by a conductor, a cur¬ 
rent flows in the external 
circuit from the chocolate- 
colored plate, which is called 
the positive electrode , to the 
other one, called the negative; the lead peroxide is 
reduced to spongy lead on the positive plate, while some 
lead sulphate is formed on the negative. During 
subsequent charging this lead sulphate is reduced by 
the hydrogen to spongy lead. Note that the charging 


Figure 391. — Charging and Dis¬ 
charging Storage Cell. 





















378 


ELECTRIC CURRENTS 


current passes through the storage cell in the opposite 
direction to the discharge current furnished by the cell 
itself. 

The storage battery stores energy and not electricity. The 
energy of the charging current is converted into the poten¬ 
tial energy of chemical separation in 
the storage cell. When the circuit of 
the charged secondary cell is closed, 
the potential chemical energy is re¬ 
converted into the energy of an electric 
current in precisely the same way as in 
a primary cell. 

Figure 392 shows a complete storage 
cell containing one positive and two 
negative plates. 

463. The Edison Storage Cell. — The 

positive electrode of this cell consists 
Figure 392. — Stor- of hydrated nickel oxide packed in a 
Plates LL WI ™ Three steel grid; the negative, of finely di¬ 
vided iron packed in another grid. 
The electrolyte is a solution of caustic potash. During 
the discharge the iron is oxidized and the nickel oxide is 
reduced. These cells are lighter and stronger than lead 
storage cells and they may be charged more rapidly; but 
their E.M.F. is lower and their efficiency less. 

III. OHM’S LAW AND ITS APPLICATIONS 

464. Resistance. — Every conductor presents some ob¬ 
struction to the passage of electricity. This obstruction 
is called its electrical resistance. The greater the con¬ 
ductance of a conductor the less its resistance, the one 
decreasing in the same ratio as the other increases. 
Resistance is the reciprocal of conductance. If It is the 






EFFECT OF HEAT ON RESISTANCE 


379 


resistance of a conductor and C its conductance, then 



465. Unit of Resistance. —The primary standard unit of 
resistance is the ohm. It is represented by the resistance 
of a uniform thread of mercury 106.3 cm. long and 14.5421 
g. in mass , at 0° C. This standard is reproducible because 
mercury can be obtained in great purity. 

A commercial standard for practical purposes consists 
of a resistance coil of suitable wire, adjusted to be exactly 
equal to the primary legal mercury standard at some 
definite temperature. 

466. Laws of Resistance.—1. The resistance of a con¬ 
ductor is proportional to its length. For example, if 39 ft. 
of No. 24 copper wire (B. & S. gauge) have a resistance 
of 1 ohm, then 78 ft. of the same wire will have a resist¬ 
ance of 2 ohms. 

2. The resistance of a conductor is inversely propor¬ 
tional to its cross sectional area. In the case of round wire 
the resistance is therefore inversely proportional to the 
square of the diameter. For example, No. 24 copper wire 
has twice the diameter of No. 30. Then 39 ft. of No. 24 has 
a resistance of 1 ohm, and 9.75 ft. of No. 30 (one-fourth 
of 39) also has a resistance of 1 ohm, both at 22° C. 

3. The resistance of a conductor of given length and 
cross section depends upon the material of which it is 
made, that is, upon the specific resistance , or resistivity of 
the material. For example, the resistance of 2.2 ft. of No. 
24 German silver wire is 1 ohm, while it takes 39 ft. of cop¬ 
per wire of the same diameter to give the same resistance. 

467. Effect of Heat on Resistance. — Changes of tempera¬ 
ture affect temporarily the resistance of metals, but all 
metals are not affected to the same extent. Nearly all 


380 


ELECTRIC CURRENTS 


pure metals show an increase in resistance of about 0.4 
per cent for a rise of temperature of 1° C., or 40 per cent 
for 100°. 

When metals are cooled in liquid air, their resistance 
falls greatly. The experiments of Dewar and Fleming 
show that the decrease in resistance of all pure metals is 
such that at the absolute zero, — 273° C., they tend to 
become perfect conductors. Recently Kamerlingh Onnes 
has found that in liquid helium, — 269° C., tin and lead 
lose all appreciable resistance and become what he calls 
super-conductors. A current started by induction in a 
closed coil of lead wire continued almost undiminished for 
several hours without any electromotive force. It con¬ 
tinued to flow as if by its inertia without encountering 
resistance. 

The resistance temperature coefficient of alloys is smaller 
than that of pure metals. That of German silver is only 
0.00044 for 1° C., that is, one-tenth that of the pure metals. 
Such alloys as manganin and constantan have practically 
no temperature coefficient. This property makes them 
very useful for resistance coils. 

The resistance of carbon and of electrolytes, unlike that 
of metals, falls on heating. The resistance of the filament 
of a carbon incandescent lamp (16 candle power), which 
is some 400 ohms when cold, is only 220 ohms when white 
hot. 

468. Eornmla for Resistance. — The above laws are con¬ 
veniently expressed in the following formula for the re¬ 
sistance of a wire: 


in which k is a constant depending on the material, l the 
length of the wire in feet, and C.M. denotes “circular 



ELECTROMOTIVE FORCE 


381 


mils.” A “mil” is a thousandth of an inch, and circular 
mils are the square of the mils ; that is, the square of the 
diameter of the wire in thousandths of an inch. For ex¬ 
ample, if the diameter of a wire is 0.020 in., then in mils it 
is 20, and the circular mils (C.M.) will be the square of 
20 or 400. Now if the length of a wire conductor is ex¬ 
pressed in feet and its cross section in circular mils, then 
it is easy to give to k for each kind of conductor such a 
value that R in the above formula will be in ohms. 

The following are the values of k in ohms for several 
metals, at 20° C.: 

Silver 9.53 Iron 61.3 German silver 181.3 

Copper 10.19 Platinum 70.5 Mercury 574.0 

469. Strength of Current. — The strength or intensity of 
a current is measured by the magnitude of the effects pro¬ 
duced by it. Any such effect may be made the basis of a 
system of measurement. The quantity of an ion deposited 
in a second is a convenient one to use in defining unit 
strength of current. The unit of current strength is the 
ampere . It is defined as the current which will deposit by 
electrolysis, under suitable conditions, 0.001118 g. of silver 
per second. The ampere deposits 4.025 g. of silver in one 
hour. A milliampere is a thousandth of an ampere. It is 
to be noted that the electrolytic method measures only the 
quantity of electricity passing through the decomposing 
cell, called a voltameter , or a coulometer , in the given time. 

470. Electromotive Force is the cause of an electric flow. 
It is often called electric pressure from its superficial anal¬ 
ogy to water pressure. The unit of electromotive force 
(E.M.F.) is the volt. A volt is the E.M.F. which will cause 
a current of one ampere to flow through a resistance of one 
ohm. The E.M.F. of a voltaic cell depends upon the ma- 


382 


ELECTRIC CURRENTS 


terials employed, and is entirely independent of the size 
and shape of the plates. The E.M.F. of a Daniell cell 
and of a gravity cell is about 1.1 volts; of a Leclanche 
and of a dry cell, 1.5 volts; of a lead storage cell, 2 volts. 

The practical international standard of electromotive 
force is the Weston Normal Cell. The electrodes are cad¬ 
mium amalgam for 
the negative and 
mercury for the 
positive. The elec¬ 
trolyte is a satu¬ 
rated solution of 
cadmium sulphate, 

and the depolarizer 
Figure 393. — Weston Normal Cell. . 

is mercurous sul¬ 
phate (Fig. 893). The E.M.F. of the Weston cell in 
volts is given by the following equation, the temperature 
t being in centigrade degrees : 

E = 1.0183 - 0.00004 (t - 20°). (Equation 35) 

471. Ohm’s Law.—The definite relation existing be¬ 
tween strength of current, resistance, and E.M.F. is 
known as Ohm's Law: 

The strength of a current equals the electromotive force 
divided by the resistance; then 

current in amperes = — O potential difference} in voUs 

resistance in ohms 

rr 

or in symbols, 7= -.(Equation 36) 

where I is the current in amperes, E the E.M.F. in volts, 
and R the resistance in ohms. Applied to a battery, if 













Alessandro Volta (1745- 

1827) was born at Como, It¬ 
aly. He was professor of 
physics at the University of 
Pavia, and was noted for his 
researches and investigations 
in electricity. The voltaic 
cell, the electroscope, the 
electrical condenser, and the 
electrophorus are due to his 
genius. 


Georg Simon Ohm (1789- 
1854) was born in Erlangen, 
Bavaria, and was educated 
at the University of that 
town. He began his inves¬ 
tigations by measuring the 
electrical conductivity of 
metals. In 1827 he an¬ 
nounced the electrical law 
named in his honor, and in 
1842 he was elected to a pro¬ 
fessorship in the University 
of Munich, 

































... - -V • 
























t , 






























CONNECTING IN SERIES 


383 


r is the resistance external to the cell, and r' the internal 
resistance of the cell itself, then 

I— ~~~7‘ • • • • (Equation 87) 

From Equation 36, E = IB and U — 

472. Methods of Varying Strength of Current. —It is evi¬ 
dent from Ohm’s law that the strength of the current 
furnished by an electric generator may be increased in 
two ways : (1) by increasing the E.M.F.; (2) by reducing 
the internal resistance. 

The E.M.F. may be increased by joining several cells 
in series and the internal resistance may be diminished by 
connecting them in parallel . 

Enlarging the plates of a bat¬ 
tery or bringing them closer 
together diminishes the in¬ 
ternal resistance. 

473. Connecting in Series. — 

To connect cells in series, join 
the positive electrode of one 
to the negative electrode of 
the next, and so on until all 
are connected. The electrodes 
of the battery thus connected in series are the positive 

electrode of the last one in the series 

, and the negative electrode of the first 

one (Fig. 394). Figure 395 is the 

conventional sign for a single cell; 

Figure 396 shows four cells in series. 

When n similar cells are connected 
Figure 395 . — Sign for . . 

Single Cell. in series, the E.M.I. of the battery is 




Figure 394 . — Cells Connected 
in Series. 
















384 


ELECTRIC CURRENTS 


n times that of a single cell; the resistance is also n times 
the resistance of one cell. Hence, by Ohm’s law for n 

cells connected in series the 
_ current is 

Xi i 11 ^ i= nE 


r 4- nr' 

To illustrate, if four cells, 
each having E.M.F. of 2 volts 
and an internal resistance of 
0.5 ohm, are joined in series 
with an external resistance of 10 ohms, the current will be 


Figupe 396. — Four Cells in 
Series. 


I— 


4x2 

10 + 4 x 0.5 


= 0.67 ampere. 


474. Connecting in Parallel. — When all the positive ter¬ 
minals are connected together on one side and the 
negative on the other, the 
cells are grouped in parallel 
(Fig. 397). With n similar 
cells the effect of such a 
grouping is to reduce the in¬ 
ternal resistance to ith that 
n 

of a single cell. It is equiv¬ 
alent to increasing the area 
of the plates n times. All the cells side by side contribute 
equal shares to the output of the battery. The E.M.F* 
of the group is the same as that of a single cell. 



Figure 397. — Cells in Parallel. 


Connection in parallel is used chiefly with storage cells, not for the 
purpose of reducing the internal resistance of the battery, but for the 
purpose of permitting a larger current to be drawn from it with safety 
to the cells. The ampere capacity of a storage cell depends on the area 
of the plates. If twenty amperes may be drawn from a single storage 
cell, then from two such cells in parallel forty amperes may be taken. 















JOULE'S LAW 


385 


IV. HEATING EFFECTS OF A CURRENT 


475. Electric Energy Converted into Heat. — Send an electric 
current through a piece of fine iron wire. The wire is heated, and it 
may be fused if the current is sufficiently strong. 

The conversion of electrical energy into other forms is 
a familiar fact. In the storage battery the energy of the 
charging current is converted into the energy of chemical 
separation and stored as the potential energy of the 
charged cells. In this experiment the energy of the cur¬ 
rent is transformed into heat because of the resistance 
which the wire offers. If the resistance of an electric 
circuit is not uniform, the most heat will be generated 
where the resistance is the greatest. 


Send the current from a few cells through a chain made of alter¬ 
nate pieces of iron and copper, soldered together (Fig. 398). The 
iron links may be made to c j^ 

glow red hot, while the copper r i 

ones remain comparatively 
cool. The resistance of the 
iron wire is about seven times as great as that of copper of the same 
length and gauge. Moreover, its thermal capacity is about three- 
quarters as great. Hence the rise of temperature of the iron links is 
roughly nine times as great as that of the copper ones. 


Figure 398. — Iron and Copper Links. 


476. Joule’s Law. — Joule demonstrated experimentally 
that the number of units of heat generated in a conductor 
by an electric current is proportional: 

a. To the resistance of the conductor. 

b. To the square of the strength of current. 

c. To the length of time the current flows} 


1 If H is the heat in calories, I the current strength in amperes, R the 

resistance in ohms, t the time in seconds, and 0.24 the number of calories 
equivalent to one joule, then the heat equivalent of a current is 
H— 0.24 x I 1 2 Rt calories. 



386 


ELECTRIC CURRENTS 



Figure 399.— Cartridge Fuse. 


477. Applications of Electric Heating. — Some of the more 

important applications of electric heating are the following : 

1. Electric Cautery. A thin plati¬ 
num wire heated to incandescence is 
employed in surgery instead of a knife. 
Platinum is very infusible and is not 
corrosive. 

2. Safety Fuses. Advantage is taken 
of the low temperature of fusion of some alloys, in which lead is a 
constituent, for making safety fuses to open a circuit automatically 
whenever the current becomes excessive (Fig. 

399). 

3. Electric Welding. If the abutting ends 
of two rods or bars are pressed together, while 
a large current passes through them, enough 
heat is generated at the junction, where the re¬ 
sistance is greatest, to soften and weld them to¬ 
gether. Figure 400 shows two wulded joints as 
they came from the welder. 

4. The Electric Flatiron. Figure 401 shows 
a flatiron, partly cut away, arranged to be 
heated by an electric current. The current 
enters by a flexible conductor and flows through 
the resistance coil E on the base of the iron. 

A is a wooden handle to avoid the use of a holder. The resistance 

.4^ is often arranged so as to con¬ 

centrate the heat at the point 
of iron. 

5. Electric Heating. Electric 
street cars are often heated by a 
current through suitable resist- 
Similar devices for cook- 


ances. 

ing are now articles of com¬ 
merce. Small furnaces for fus¬ 
ing, vulcanizing, and enameling 
are common in dentistry. 

Large furnaces are employed 



Figure 400. — Elec- 
trically Welded 
Joints. 



Figure 401.— Electric Flatiron. 
for melting refractory substances, for the reduction of certain ores, 
and for chemical operations demanding a high temperature. 


























































MAPPING THE MAGNETIC FIELD 


387 


V. MAGNETIC PROPERTIES OF A CURRENT 

478. Magnetic Field Around a Conductor. — Dip a portion of 
a wire carrying a heavy current into fine iron filings. A thick cluster 
of them will adhere to the 

wire (Fig. 402) ; they will ^ . .a 

drop off as soon as the cir- Figure 402. — Magnetic Field around a 
cuit is opened. Current. 

The experiment shows that a conductor through which 
an electric current is passing.has mag¬ 
netic properties. The iron filings are 
magnetized by the current and set 
themselves at right angles to the wire. 
When the circuit is broken, they lose 
their magnetism and drop off. 

479. Mapping the Magnetic Field. — 

Support horizontally a sheet of cardboard or 
of glass LB with a hole through it. Pass 
vertically through the hole a wire, W, con¬ 
necting with a suitable electric generator, so 
that a strong current can be sent through 
the circuit (Fig. 403). Close the circuit and 
sift iron filings on the paper or glass about the wire, jarring the sheet 
by tapping it. The filings will ar¬ 
range themselves in circular lines 
about the wire. Place a small 
mounted magnetic needle on the 
sheet near the wire; it will set itself 
tangent to the circular lines, and if 
the current is flowing downward, the 
north pole will point in the direction 
in which the hands of a watch move. 

The lines of magnetic force 
about a wire through which an 
electric current is flowing, are 
concentric circles. Figure 404 



Magnetic Field. 



Figure 404. — Circular Lines of 
Force around a Wire. 

















888 


ELECTRIC CURRENTS 


was made from a photograph of these circular lines of force 
as shown by iron filings on a plate of glass. Their direc¬ 
tion relative to the current 
is given by the following 
rule: 

G-rasp the wire by the right 
hand so that the extended thumb 
points in the direction of 
Figure 405.'— Fingers show Direc- the current; then the fingers 
tion of Lines of Force. wrapped around the wire indi¬ 
cate the direction of the lines of force (Fig. 405). 

Figure 406 is a sketch intended to show the direction of 


<—<mc 


Figure 406. — Magnetic Whirl. 

these circular lines of magnetic force (or magnetic whirl) 
which everywhere surround a wire conveying a current. 

480. Properties of a Circular Con¬ 
ductor. — Bend a copper wire into the form 
shown in Figure 407, the diameter of the cir¬ 
cle being about 20 cm. Suspend it by a long 
untwisted thread, so that the ends dip into 
the mercury cups shown in cross section in 
the lower part of the figure. Send a cur¬ 
rent through the suspended wire by connect¬ 
ing a battery to the binding posts. A bar 
magnet brought near the face of the circular 
conductor will cause the latter to turn about 
a vertical axis and take up a position with 
its plane at right angles to the axis of the 
magnet. With a strong current the circle 
will turn under the influence of the earth’s 
magnetism. 



MiMSHIXb* 


Figure 407. — Deflec¬ 
tion of Circular Cur¬ 
rent by a Magnet. 















POLARITY OF A HELIX 


389 


This experiment shows that a circular current acts like 
a disk magnet, whose poles are its faces. The lines 
of force surrounding the conductor in this form pass 
through the circle and around from one face to the other 
through the air outside the loop. The 
north-seeking side is the one from 
which the lines issue; and to an ob¬ 
server looking toward the side, the 
current flows around the loop counter¬ 
clockwise (Fig. 408). 

If instead of a single turn we take a 
long insulated wire and coil it into a 
number of parallel circles close to¬ 
gether, the magnetic effect will be in¬ 
creased. Such a coil is called a helix 
or solenoid; and the passage of an electric current through 
it gives to it all the properties of a cylindrical bar magnet. 



Figure 408. — Lines 
of Force through a 
Loop. 


Thread a loose coil of copper wire through holes in a sheet of mica, 
so that each turn lies half on one side and half on the other (Fig. 409). 

Place horizontally and scatter fine 
iron filings evenly over the mica. 
Send a strong current through the 
coil and gently tap the mica. The 
filings will gather in the general 
direction of the lines of force 
through the helix. 

481. Polarity of a Helix.— 

The polarity of a helix may 
be determined by the follow- 
Figure 409. — Field in Helix. ing rule: 

G-rasp the coil with the right hand so that the fingers point 
in the direction of the current ; the north pole will then he in 
the direction of the extended thumb. 






390 


ELECTRIC CURRENTS 



Figure 410. — Action between 
Two Circuits. 


482. Mutual Action of Two Currents. — Make a rectangular 
coil of insulated copper wire by winding four or five layers around 

the edge of a board about 25 cm. square. 
Slip the wire off the board and tie the 
parts together in a number of places 
with thread. Bend the ends at right 
angles to the frame, remove the insula¬ 
tion, and give them the shape shown in 
Figure 410. Suspend the wire frame by 
a long thread so that the ends dip into 
the mercury cups. 

Make a second similar but smaller 
coil and connect it in the same circuit 
with the rectangular coil and a battery. 

First. Hold the coil HK with its 
plane perpendicular to the plane of the 
coil EF, with its edge H parallel to F, 
and with the currents in these two ad¬ 
jacent portions flowing in the same direction. The suspended coil will 
turn upon its axis, the edge F approaching H, as if it were attracted. 

Second. Reverse HK so that the currents in 
the adjacent portions K and F flow in opposite 
directions. The edge F of the suspended coil will 
be repelled by K. 

Third. Hold the coil HK within EF, so that 
their lower sides form an angle. EF will turn 
until the currents in its lower side are parallel 
with those in H, and flowing in the same direction. 

Mount a long flexible helix as in Figure 411, 
with the free end just dipping into the mercury 
in the glass cup. Pass a sufficient current through 
it; it will shorten because of the attraction be¬ 
tween parallel turns, until the lower end leaves 
the mercury and breaks the circuit. It will then 
lengthen and close the circuit ready for another Attraction between 
oscillation. Turns. 



Figure 411. — 


These facts may be summarized in the following laws of 
action between currents: 















MAGNETIC FIELDS ABOUT PARALLEL CURRENTS 391 


1 • Parallel cur¬ 
rents flowing in the 
same direction at¬ 
tract. 

II. Parallel cur¬ 
rents flowing in op¬ 
posite directions re¬ 
pel. 

III. Currents 
making an angle 
with each other tend 
to become parallel 
tion. 



Figure 412. — Magnetic Field about Paral¬ 
lel Currents in the Same Direction. 

and to flow in the same direc- 



483. Magnetic Fields about Parallel Currents. — Figure 412 
was made from a photograph of the magnetic field about 
two parallel currents in the same direction perpendicular 
to the figure. Many of these lines of force surround both 
wires, and it is the tension along them that draws the 
wires together. Figure 413 was made from a photograph 

of the field when 
the currents were 
in opposite direc¬ 
tions. The lines of 
force are crowded 
together between 
the wires, and their 
reaction in their 
effort to recover 
their normal posi- 
„ „ tion forces the 

Figure 413. — Magnetic Field about Parallel 

Currents in Opposite Directions. Wires apart. 





392 


ELECTRIC CURRENTS 


VI. ELECTROMAGNETS 

484. Effect of Introducing Iron into a Solenoid. — Fill the 

lower half of the helix of § 480 with soft straight iron wires, and 
again pass the same current as before through the coil. The mag¬ 
netic field will be greatly strengthened by the iron. 

A helix of wire about an iron core is an electromagnet . 
It was first made by Sturgeon in 1825. The presence of 
the iron core greatly increases the number of lines of force 
threading through the helix from end to end, by reason of 



Figure 414. — Iron Increases Magnetic Lines. 


the greater permeability of iron as compared with air 
(Fig. 414). If the iron is omitted, there are not only 
fewer lines of force, but because of their leakage at the 
sides of the helix, fewer traverse the entire length of 
the coil. 

The soft iron core of an electromagnet does not show 
much magnetism except while the current is flowing 
through the magnetizing coil. The loss of magnetism is 
not quite complete when the current is interrupted; the 
small amount remaining is called residual magnetism. 

485. Relation between a Magnet and a Flexible Conductor. 

— Iron filings arranged in circles about a conductor may be regarded 
as flexible magnetized iron winding itself into a helix around the 
current; conversely, a flexible conductor, carrying a current, winds 








James Clerk-Maxwell (1831-1879) was a remarkable physi¬ 
cist and mathematician. He was born in Edinburgh and studied 
in the University of that city. Later he attended the University 
of Cambridge, graduating from there in 1854. In 1856 he be¬ 
came professor of natural philosophy at Marischal College, Aber¬ 
deen, and in 1860 professor of physics and astronomy at King’s 
College, London. In 1871 he was appointed professor of experi¬ 
mental physics in Cambridge. His contributions to the kinetic 
theory of gases, the theory of heat, dynamics, and the mathemati¬ 
cal theory of electricity and magnetism are imperishable monu¬ 
ments to his great genius and wonderful insight into the mysteries 
of nature. 








































































































































































. 




































THE HORSESHOE MAGNET 


393 


itself around a straight bar magnet. The flexible conductor of 
Figure 415 may be made of tinsel cord or braid. Directly the circuit is 
closed, the conductor winds 
slowly around the vertical mag¬ 
net ; if the current is then re¬ 
versed, the conductor unwinds 
and winds up again in the re¬ 
verse direction. 

486. The Horseshoe Mag¬ 
net. — The form given to 
an electromagnet depends 
on the use to which it is to 
be put. The horseshoe or 
U-shape (Fig. 416) is the 
most common. The ad¬ 
vantage of this form lies 
in the fact that all lines of 
magnetic force are closed 
curves, passing through the 
core from the south to the 
north pole, and completing the circuit through the air from 
the north pole back to the south pole. The U-shape lessens 
the distance through the air and thus increases the number 

of lines. Moreover, when an iron 
bar, called the armature , is placed 
across the poles, the air gap is re¬ 
duced to a thin film, the number 
of lines is increased to a maximum 
with a given current through the 
helix, and the magnet exercises 

Figure 416. — Horseshoe g rea test pull on the arma- 

Magnet. & r 

ture. 

When the armature is in contact with the poles, the 
magnetic circuit is all iron, and is said to be a closed 




Figure 415. — Flexible Conductor 
Winds itself around a Magnet. 




















394 


ELECTRIC CURRENTS 


magnetic circuit. The residual magnetism is then much 
greater than in the case of an open magnetic circuit with 
an air gap. 

Bring the armature in contact with the iron poles of the core, and 
close the electric circuit; after the circuit is opened, the armature will 
still cling to the poles and can be removed only with some effort. 
Then place a piece of thin paper between the poles and the armature. 
After the magnet has again been excited and the circuit opened, the 
armature will not now “ stick.” The paper 
makes a thin air gap between the poles of the 
magnet and the armature, and thus reduces 
the residual magnetism. 

487. Applications of Electromagnets.— 
The uses to which electromagnets are put in 
the applications of electricity are so numerous 
that a mere reference to them must suffice. 
The electromagnet enters into the construc¬ 
tion of electric bells, telegraph and telephone 
instruments, dynamos, motors, signaling de¬ 
vices, etc. It is also extensively used in lift¬ 
ing large masses of iron, such as castings, 
rolled plates, pig iron, and steel girders (Fig. 
417). The lifting power depends chiefly on 
the cross section of the iron core and on the 
ampere turns ; that is, on the product of the 
number of amperes of current and the number of turns of wire 
wound on the magnet. 

VII. MEASURING INSTRUMENTS 

488. The Galvanometer. — The instrument for the com¬ 
parison of currents by means of their magnetic effects is 
called a galvanometer. A galvanoscope (§ 446) becomes 
a galvanometer by providing it with a scale so that the 
deflections may be measured. If the galvanometer is 
calibrated, so as to read directly in amperes, it is called an 
ammeter. In very sensitive instruments a small mirror is 



THE D'ARSONVAL GALVANOMETER 


395 


attached to the movable part of the instrument; it is then 
called a mirror galvanometer. Sometimes a beam of light 
from a lamp is reflected from this 
small mirror back to a scale, and 
sometimes the light from a scale 
is reflected back to a small tele¬ 
scope, by means of which the de¬ 
flections are read. In either case 
the beam of light then becomes a 
long pointer without weight. 

489. The d’Arsonval Galvanom¬ 
eter.— One of the most useful 
forms of galvanometer is the 
d’Arsonval. The plan of it is 
shown in Figure 418 and a com¬ 
plete working instrument in Figure 419. 
Between the poles of a strong permanent 
magnet of the horseshoe form swings a 
rectangular coil of fine wire in such a way 
that the current is led into the coil by the 
fine suspending wire, and out by the wire 
spiral running to the base. A small mirror 
is attached to the coil to reflect light from 
a lamp or an illuminated scale. Some¬ 
times the coil carries a light aluminum 
pointer, which traverses a scale. Inside 
the coil is a soft iron tube supported from 
the back of the case. It is designed to 
Simple d’Arson- concentrate the lines of force in the narrow 
val Galvanom- 0 p en i n g S between it and the poles of the 
magnet. 

In the d’Arsonval galvanometer the coil is movable and 
the magnet is fixed. Its chief advantages are simplicity 




sonval Galvanometer. 























396 


ELECTRIC CURRENTS 



Figure 420. — Voltmeter. 


of construction, comparative independence of the earth’s 
magnetic field, and the quickness with which the coil 
comes to rest after deflection by a current through it. 

490. The Voltmeter. 
— The voltmeter is an 
instrument designed to 
measure the difference 
of potential in volts. 

S tep® For direct currents the 

most convenient port- 

_able voltmeter is made 

on the principle of the 
d’Arsonval galvanom¬ 
eter. One of the best- 
known instruments of 
this class is shown in Figure 420. The interior is rep¬ 
resented by Figure 421, where a portion of the in¬ 
strument is cut away to show the coil and the springs. 
The current is led in by one spiral spring and out by 
the other. Attached to the 
coil is a very light aluminum 
pointer, which moves over 
the scale seen in Figure 420 
where it stands at zero. Soft 
iron pole pieces are screwed 
fast to the poles of the per¬ 
manent magnet, and they are 
so shaped that the divisions 
of the scale in volts are equal. 

In circuit with the coil of 
,, . , , . r Figure 421. — Inside of Voltmeter. 

the instrument is a coil of 

wire of high resistance, so that when the voltmeter is placed 
in circuit, only a small current will flow through it. 








DIVIDED CIRCUITS—SHUNTS 


397 


491. The Ammeter, designed to measure electric currents 
in amperes, is very similar in construction to the voltmeter. 
A low resistance shunt is connected across the terminals 
of the coil to carry the main current, so that when the 
ammeter is placed in circuit, it will not change the value 
of the current to be measured. 

Questions 

1. Why must the article to be electroplated be attached to the 
negative pole of the generator ? 

2. How can you determine the positive pole of a storage battery ? 

3. Why will it ruin a pocket ammeter to connect its terminals to 
the poles of a storage battery ? 

4. Why does the heating in an electric circuit manifest itself at a 
point where the conductor is defective? 

5. If in Figure 415 the north pole of the magnet is at the top, 
which way will the flexible tinsel wrap around the magnet? 

6. Why should the ammeter be of low resistance and the volt¬ 
meter of high resistance ? 

7. Why should a Daniell cell when not in use either be taken 
down or placed on closed circuit ? 

8. Why must the wire used in winding an electromagnet be 
insulated ? 

9. What is the least number of gravity cells that might be used 
to charge a storage battery and how must they be connected? 

10. What would be the harm of leaving a dry cell on a closed 
circuit ? 

11. Why will a low resistance voltmeter give the E.M.F. of a 
storage battery more nearly correct than it will that of a dry cell? 

12. Why will cotton-wound wire be sufficiently insulated for a 
battery, but not for a Holtz machine ? 

492. Divided Circuits — Shunts. — When the wire leading 
from any electric generator is divided into two branches, 
as at B (Fig. 422), the current also divides, part flowing 


398 


ELECTRIC CURRENTS 


by one path and part by the other. The sum of these two 
currents is always equal to the current in the undivided 

part of the circuit, since there 
is no accumulation of electric¬ 
ity at any point. Either of 

_ „ the branches between B and 

Figure 422. — Divided Circuit. . . __ _ 7 , 

A is called a shunt to the 

other, and the currents through them are inversely propor¬ 
tional to their resistances. 

493. Resistance of a Divided Circuit. — Let the total resist¬ 
ance between the points A and B (Fig. 422) be represented by R, 
that of the branch BmA by r, and of BnA by r'. The conductance of 
BA equals the sum of the conductances of the two branches; aud, as 
conductance is the reciprocal of resistance, the conductances of BA, 

BmA, and BnA are—, and — respectively; then — =i + —. 

R r r' R r r' 

From this we derive R = — • To illustrate, let a galvanometer 

whose resistance is 100 ohms have its binding posts connected by a 
shunt of 50 ohms resistance; then the total resistance of this divided 

circuit is ^ X ^ = 334 ohms. 

100 + 50 3 

The introduction of a shunt 
always lessens the resistance be¬ 
tween the points connected. 

494. Loss of Potential 

along a Conductor. — Stretch 
a fine wire of fairly high resist¬ 
ance, such as a German silver 
No. 30, along the edge of a meter 
stick (Fig. 423). Connect the 
ends P and Q to a storage cell 423. -Fall ofPotent,alalong 

with a contact key in circuit. 

At P connect a galvanometer in circuit with a high resistance R and 
a slide contact S. The galvanometer will indicate the difference of 
potential between P and S , the point of contact on PQ. If S be 
placed successively on PQ at 10 cm., 20 cm., 30 cm., etc., from P, and 






v •/ v */ </ •/ </ </ v y w v 

















W HE A T STONE'S BRIDGE 


399 


the galvanometer reading be recorded each time, the ratio of the 
readings will be as 1:2:3, etc. Since resistance is proportional to 
length, these potential differences are as the resistances of the succes¬ 
sive lengths of the wire PQ , or the loss of potential is proportional to the 
resistance passed over. 

This is equivalent to another statement of Ohm’s law; 

JE 

for since I = —, and the current through the conductor is 
R 

the same at all points, it follows that R must vary as R to 
make I constant. 


495. Wheatstone’s Bridge. — The Wheatstone’s Bridge is a de¬ 
vice for measuring resistances. The four conductors, R v R 2 , R s , R 4 
are the arms and BD the bridge (Fig. 

424). When the circuit is closed by 
closing the key jfif 2 , the current divides 
at A, the two parts reuniting at C. 

The loss of potential along ABC is the 
same as along ADC. If no current 
flows through the galvanometer G 
when the key if, is also closed, then 
there is no potential difference between 
B and D to produce a current. Under 
these conditions the loss of potential 
from A to B is the same as from A 
to D. We may then get an expression 
for these potential differences and 
place them equal to each other. 

Let 7j be the current through R x ; it will also be the current 
through R 4 , because none flows across through the galvanometer. 
Also let I 2 be the current through the branch ADC. Then the poten¬ 
tial difference between A and B by Ohm’s law (§ 471) is equal to R\h ; 
and the equal potential difference between A and D is R 2 I 2 . Equating 
these expressions, = jy f .(„) 

In the same way the equal potential differences between B and C 

RJ i = R,h ..( b ) 



Figure 424. — Wheatstone’s 
Bridge. 


and D and C give 








400 


ELECTRIC CURRENTS 


Dividing (a) by ( b ) gives 

^ *.(Equation 38) 

R s 

In practice three of the four resistances are adjustable and of 
known value. They are adjusted until the galvanometer shows no 
deflection when the key K\ is closed after key K 2 . The value of the 
fourth resistance is then derived from the relation in Equation 38. 

Problems 

1. Calculate the resistance of 200 ft. of copper wire (Jc = 10.19) 
No. 24 (diameter = 0.0201 in.). 

2. A coil of iron wire (Jc = 61.3) is to have a resistance of 25 ohms. 
The diameter of the wire used is 0.032 in. How many feet will it re¬ 
quire ? 

3. What diameter must a copper trolley (Jc = 10.19) have so that 
the resistance will be half an ohm to the mile? 

4. A current of one ampere deposits by electrolysis 1.1833 g. of 
copper in an hour. How long will it take a current of 5 amperes to 
deposit a kilogram of copper ? 

5. A current of two amperes passes through a solution of silver 
nitrate for one hour. How much silver will be deposited ? 

6 . A current of 10 amperes is sent through a resistance of 4 ohms 
for 10 minutes. How many calories of heat are generated? 

7. What current will 6 dry cells connected in series, each having 
an E.M. F. of 1.5 volts and an internal resistance of 0.1 ohm, give 
through an external resistance of 2 ohms ? 

8. A certain dry cell has a voltage of 1.5 volts and when tested 
with an ammeter gives 20 amperes. What is its internal resistance ? 

9. A certain lamp requires 0.5 ampere current and an E.M. F. of 
110 volts to light it. What is its resistance ? 

10 . A projection lantern requires a current of 15 amperes. The 
voltage of the supply is 110 volts and the loss in the lamp is 40 volts. 
What resistance must be inserted in the line to the lantern? 




Joseph Henry (1797-1878) was born at Albany, New York. 
The reading of Gregory’s Lectures on Experimental Philosophy 
interested him so greatly in science that he began experimenting. 
In 1829 he constructed his first electromagnet. In 1832 he was 
appointed professor of natural philosophy at Princeton College. 
In 1846 he became secretary of the Smithsonian Institution in 
Washington. It is almost certain that he anticipated Faraday’s 
great discovery of magneto-electric induction by a whole year 
but failed to announce it. His principal investigations were in 
electricity and magnetism, and chiefly in the realm of induced 
currents. 





Michael Faraday, 1791-1867, was born near London, England. 
He was the son of a blacksmith and received but little schooling, 
being apprenticed to a bookbinder when only thirteen years of 
age. While employed in the bindery he became interested in 
reading such scientific books as he found there. Later he applied 
to Sir Humphry Davy for consideration and was made Davy's 
assistant. From this time his rise was rapid; in 1816 he published 
his first scientific memoir; in 1824 he became a member of the 
Royal Society; in 1825 he was elected director of the Royal 
Institution; in 1831 he announced the discovery of magneto¬ 
electric induction, the most important scientific discovery of any 
age. In 1833 he was elected professor of chemistry in the Royal 
Institution. He was a remarkable experimenter and a most inter¬ 
esting lecturer, and amid all his wonderful achievements, he was 
utterly wanting in vanity. 



CHAPTER XIII 


ELECTROMAGNETIC INDUCTION 

I. FARADAY’S DISCOVERIES 

496. Electromotive Force Induced by a Magnet. — Wind a 
large number of turns of fine insulated wire around the armature of a 
horseshoe magnet, leaving the ends of the iron free to come in contact 
with the poles of the permanent 
magnet. Connect the ends of the 
coil to a sensitive galvanometer, 
the armature being in contact 
with the magnetic poles, as shown 
in Figure 425. Keeping the mag- Figure 425 . _ Faraday’s Original 
net fixed, suddenly pull off the ar- Experiment on Induced E. M. F. 
mature. The galvanometer will 

show a momentary current. Suddenly bring the armature up against 
the poles of the magnet; another momentary current in the reverse 
direction will flow through the circuit. This experiment illustrates 

Faraday’s original method 
of producing an electric 
current through the 
agency of magnetism. 

Connect a coil of insu¬ 
lated copper wire, at least 
fifty turns of No. 24, in 
circuit with a d’Arsonval 
galvanometer (Fig. 426). 
Thrust quickly into the 
coil the north pole of a 
bar magnet. The galva¬ 
nometer will show a transient current, which will flow only during 
the motion of the magnet. When the magnet is suddenly withdrawn 

401 



Figure 426. —Current Induced by Thrust¬ 
ing Magnet into Coil. 











402 


ELECTR OMA GNETIC IND UCTION 


a transient current is produced in the opposite direction to the first 
one. If the south pole be thrust into the coil, and then withdrawn, 
the currents in both cases are the reverse of those with the north pole. 
If we substitute a helix of a smaller number of turns, or a weaker bar 
magnet, the deflection will be less. 

The momentary electromotive forces generated in the 
coil are known as induced electromotive forces, and the cur¬ 
rents as induced currents. They were discovered by 
Faraday in 1831. 

497. Laws of Electromagnetic Induction. — When the 
armature in the first experiment of the last article is in 
contact with the poles of the magnet, the number of lines 
of force passing through the coil, or linked with it, is a 
maximum. When the armature is pulled away, the num¬ 
ber of magnetic lines threading through the coil rapidly 
diminishes. 

When the magnet in the second experiment is thrust 
into the coil, it carries its lines of force with it, so that 
some of them at least encircle, or are linked with, the 
wires of the coil. In both experiments an electromotive 
force is generated only while the number of lines so linked 
with the coil is changing. The E.M.F. is generated in 
the coil iii accordance with the following laws : 

I. An increase in the number of lines of force linked 
with a conducting circuit -produces an indirect E. M. F.; 
a decrease in the number of lines produces a direct E. M. F. 

II. The induced E. M. F. at any instant is equal to the 
rate of increase or decrease in the number of lines of force 
linked with the circuit. 

A direct E.M.F. has a clockwise direction to an observer 
looking along the lines of force of the magnet; an indirect 
E. M. F. is one in the opposite direction. Thus, in Figure 


INDUCTION BY CURRENTS 


403 


427 the north pole of the magnet is moving into the coil 
in the direction of the arrow ; there is an increase in 


the number of lines passing 
through the coil, and the E. 
M.F. and current are indirect 
or opposite watch hands, as 
shown by the arrows on the 
coil, to an observer looking 
at the coil in the direction 
of the arrow on the magnet. 




498. Induction by Currents. F,0URE 4 ^- D ^™ N 0F lN ' 

— Connect the S coil of Figure 428 

to a d’Arsonval galvanometer, and a second smaller coil P to the 
terminals of a battery. If the current through P is kept constant, 

, when P is made to approach 

S an E. M. F. is generated in 
S tending to send a current 
Jpl^ iii a direction opposite to the 
current around P; removing 
the coil P generates an oppo- 
P |S@ p site E.M.F. These E. M. F.’s 

act $ only so long as P is 

battery . Next insert the coil P in S 
with the battery circuit open. 

S ifiiiiiilPi If then the battery circuit is 

closed, the needle of the gal¬ 
vanometer will be deflected, 
: : but will shortly come again to 

rest at zero. The direction 
of this momentary current is 
opposite to that in P. Open¬ 
ing the battery circuit produces 
another momentary current 
through S but in the opposite 
direction. Increasing and decreasing the current through P has the 
same effect as closing and opening the circuit. 


To galva¬ 
nometer 


Figure 428. — Currents Induced by 
Another Current. 



404 


ELECTROMAGNETIC INDUCTION 


If while P is inside 5 with the battery circuit closed, a bar of soft 
iron is placed within P, there is an increase of magnetic lines through 
both coils and the inductive effect in S is the same as that produced 
by closing the circuit through P. 

The coil P is called the ‘primary and S the secondary 
coil. The results may be summarized as follows: 

I. A momentary current in the opposite direction is 
induced in the secondary conductor by the approach , the 
starting, or the strengthening of a current in the primary. 

II. A momentary current in the same direction is in¬ 
duced in the secondary by the receding, the stopping , or 
the weakening of the current in the primary. 

The primary coil becomes a magnet when carrying an 
electric current (§ 480) and acts toward the secondary coil 
as if it were a magnet. The soft iron increases the 
magnetic flux through the coil and so increases the in¬ 
duction. 

499. Lenz’s Law. — When the north pole of the magnet is 
thrust into the coil of Figure 427, the induced current flow¬ 
ing in the direction of the arrows produces lines of force 
running in the opposite direction to those from the magnet 
(§ 479). These lines of force tend to oppose the change 
in the magnetic field within the coil, or the magnetic field 
set up by the coil opposes the motion of the magnet. 

Again, when the primary coil of Figure 428 is inserted 
into the secondar}^, the induced current in the latter is 
opposite in direction to the primary current, and parallel 
currents in opposite directions repel each other. In every 
case of electromagnetic induction the change in the mag¬ 
netic field which produces the induced current is always 
opposed by the magnetic field due to the induced current 
itself. 


JOSEPH HENRY'S DISCOVERY 


405 


The law of Lenz respecting the direction of the induced 
current is broadly as follows: 

The direction of an induced current is always such 
that it produces a magnetic field opposing the motion or 
change which induces the current. 

II. SELF-INDUCTION 

500. Joseph Henry’s Discovery.—Joseph Henry discov¬ 
ered that a current through a helix with parallel turns 
acts inductively on its own circuit, producing what is 
often called the extra current , and 
a bright spark across the gap when 
the circuit is opened. The effects 
are not very marked unless the 
helix contains a soft iron core. 

Let a coil of wire be wound 
around a wooden cylinder (Fig. 

429). When a current is flowing 
through this coil, some of the lines Figure 429.-Self-induc- 
of force • around one turn, as A , 

thread through adjacent turns; if the cylinder is iron, the 
number of lines threading through adjacent turns will be 
largely increased on account of the superior permeability 
of the iron (§ 401). Hence, at the make of the circuit, 
the production of magnetic lines threading through the 
parallel turns of wire induces a counter-E.M.F. opposing 
the current. The result is that the current does, not reach 
at once the value given by Ohm’s law. At the break of 
the circuit, the induction on the other hand produces a 
direct E.M.F. tending to prolong the current. With 
many turns of wire, this direct E.M.F. is high enough 
to break over a short gap and produce a spark. 








406 


ELECTROMAGNETIC INDUCTION 


501. Illustrations of Self-Induction. — Connect two or three 
cells in series. Join electrically a flat file to one pole and a piece of 
iron wire to the other. Draw the end of the wire lengthwise along 
the file; some sparks will be visible, but they emit little light. Now 
put an electromagnet in the circuit to increase the self-induction; 

the spkrks are now much longer and 
brighter. 

Connect as shown in Figure 430 a large 
electromagnet M, a storage battery B, a 
circuit breaker K, and an incandescent 
lamp L of such a size that the battery 
alone will light it to nearly its full candle 
power. The circuit divides between the 
lamp and the electromagnet, and since the 
latter is of low resistance, when the cur¬ 
rent reaches its steady state most of it will 
go through the coils of the magnet, leaving 
the lamp at only a dull red. At the in¬ 
stant when the circuit is closed, the self- 
induction of the magnet acts against the 
current and sends most of it around 
through the lamp. It accordingly lights 
up at first, but quickly grows dim as the current rises to its steady 
value in M. 

Now open the circuit breaker K, cutting off the battery. The only 
closed circuit is now the one through the magnet and the lamp; but 
the energy stored in the magnetic field of the electromagnet is then 
converted into electric energy by means of self-induction, and the 
lamp again lights up brightly for a moment. 

HI. THE INDUCTION COIL 

502. Structure of an Induction Coil. —The induction coil 
is commonly used to give transient flashes of high electro¬ 
motive force in rapid succession. A primary coil of com¬ 
paratively few turns of stout wire is wound around an 
iron core, consisting of a bundle of iron wires to avoid 
induced or eddy currents in the metal of the core ; outside 



Figure 430. — Lamp 
Lighted by Self-induction 
of Magnet. 























ACTION OF THE COIL 


407 



Figure 431. — Induction Coil. 


of this, and carefully insulated from it, is the secondary of 
a very large number of turns of fine wire. The inner or 
primary coil is connected 
to a battery through a cir¬ 
cuit breaker (Fig. 431). 

This is an automatic device 
for opening and closing the 
primary circuit and is ac¬ 
tuated by the magnetism 
of the iron core. At the 
“ make ” and “ break ” of 
the primary circuit elec¬ 
tromotive forces are induced in the secondary in accord¬ 
ance with the laws of electromagnetic induction (§ 497). 
Large induction coils include also a condenser . It is 
placed in the base and consists of two sets of interlaid 
layers of tin-foil, separated by sheets of paper saturated 
with paraffin. The two sets are connected to two points 
of the primary circuit on opposite sides of the circuit 
breaker (Fig. 432). 

503. Action of the Coil. — Figure 432 shows the arrange¬ 
ment of the various parts of an induction coil. The cur¬ 
rent first passes through the heavy primary wire PP, 
thence through the spring which carries the soft iron 
block P, then across to the screw 6, and so back to the 
negative pole of the battery. This current magnetizes 
the iron core of the coil, and the core attracts the soft iron 
block P, thus breaking the circuit at the point of the 
screw b. The core is then demagnetized, and the release 
of P again closes the circuit. Electromotive forces are 
thus induced in the secondary coil SS, both at the make 
and the break of the primary. The high E.M.F. of the 
secondary is due to the large number of turns of wire in 


408 


ELECTROMA GNETIC IND UCTION 


it and to the influence of the iron core in increasing the 
number of lines of force which pass through the entire 
coil. 

The self-induction of the primary has a very important 
bearing on the action of the coil. At the instant the cir¬ 
cuit is closed, the counter E.M.F. opposes the battery 


s s 



current, and prolongs the time of reaching its greatest 
strength. Consequently the E.M.F. of the secondary 
coil will be diminished by self-induction in the primary. 
The E.M.F. of self-induction at the “break” of the pri¬ 
mary is direct, and this added to the E.M.F. of the battery 
produces a spark at the break points of the circuit breaker. 

504. Office of the Condenser. — When the primary circuit of an 
induction coil is broken, the self-induction tends to sustain the cur¬ 
rent as if it had inertia; hence it jumps the break as a spark and 
prevents the abrupt interruption of the primary current, which is 
essential to high induction in the secondary. The condenser connected 
across the break gap acts as a reservoir into which the current surges 
instead of jumping across the break. Thus the spark is nearly elimi¬ 
nated and the secondary E. M. F. increased. 

Further, after the break, the condenser, which has been charged by 
the E.M.F. of self-induction, discharges back through the primary 





























EXPERIMENTS WITH THE INDUCTION COIL 409 


coil. The condenser thus causes an electric recoil in the current in 
the reverse direction through the primary, demagnetizing the core 
and increasing the rate of change of the magnetic flux, and so in¬ 
creasing the E. M. F. in the secondary. Hence, when the secondary 
terminals are separated, the discharge is all in one direction and occurs 
when the primary current is broken. 

505. Experiments with the Induction Coil. — 1 . Physiological 
Effects. — Hold in the hands the electrodes of a very small induction 
coil, of the style used by physicians. When the coil is working, a 
peculiar muscular contraction is produced. 

The “ shock ” from large coils is dangerous on account 
of the high E.M.F. The danger decreases with the in¬ 
crease in the rapidity of the impulses or alternations. 
Experiments with induction coils, worked by alternating 
currents of very high frequency, have demonstrated that 
the discharge of the secondary up to an ampere may be 
taken through the body without injury. 

2. Mechanical Effects. — Hold a piece of cardboard between the 
electrodes of an induction coil giving a spark 3 cm. long. The card 
will be perforated, leaving a burr on each side. Thin plates of any 
nonconductor can be perforated in the same manner. 

3. Chemical Effects. — Place on a plate of glass a strip of white 
blotting-paper moistened with a solution of potassium iodide (a com¬ 
pound of potassium and iodine) and starch paste. Attach one of the 
electrodes of a small induction coil to the margin of the paper. 
With an insulator, handle a wire leading to the other electrode, and 
when the coil is in action, trace characters with the wire on the paper. 
The discharge decomposes the potassium iodide, as shown by the blue 
mark. This blue mark is due to the action of the iodine on the 
starch. 

If the current from the secondary of an induction coil be passed 
through air in a sealed tube, the nitrogen and oxygen will combine to 
form nitrous acid. This is the basis of some of the commercial 
methods of manufacturing nitrogen compounds from the nitrogen of 
the air. 

4. Heating Effects. — Figure 433 shows the plan of the “ electric 
bomb.” It is usually made of wood. Fill the hole with gun powder 


410 


ELECTROMAGNETIC INDUCTION 


as far up as the brass rods and close the mouth with a wooden ball. 
Connect the rods to the poles of the induction coil. The sparks will 


Q 



ignite the powder and the ball will 
be projected across the room. 

The heating effect of the current 
in the secondary of a large induction 
coil may be shown by stretching 
between its poles a very thin iron 
wire with a small gap in it. The 
discharge will melt the part con¬ 
nected to the negative pole of the 
coil, while the other part will re¬ 
main below the temperature of 
ignition. 

506. Discharges in Partial 


Figure 433. — Electric Bomb. 


Vacua. — Place a vase of uranium 
glass on the table of the air pump, 
under a bell jar provided with a brass sliding rod passing air-tight 
through the cap at the top (Fig. 434). Connect the rod and the air 
pump table to the terminals of the induction coil. When the air is 
exhausted a beautiful play of light will fill the 
bell jar. The display will be more beautiful if 
the vase is lined part way up with tin-foil. 

This experiment is known as Gassiot’s cascade. 

The experiment may be varied by admitting 
other gases and exhausting again. The aspect 
of the colored light will be entirely changed. 

The best effects are obtained with 
discharges from the secondary of an in¬ 
duction coil in glass tubes when the 
exhaustion is carried to a pressure of 
about 2 mm. of mercury, and the tubes 
are permanently sealed. Platinum elec¬ 
trodes are melted into the glass at the two ends. Such 
tubes are known as Geissler tubes. They are made in 
a great variety of forms (Fig. 435), and the luminous 
effects are more intense in the narrow connecting tubes 



Figure 434. — Gas¬ 
siot’s Cascade. 




























THE DISCHARGE INTERMITTENT 


411 


than in the large bulbs at the ends. The colors are de¬ 
termined by the nature of the residual gas. Hydrogen 
glows witli a brilliant crimson; the vapor of water gives 
the same color, indicating 
that the vapor is disso¬ 
ciated by the discharge. 

An examination of this 
glow by the spectroscope 
gives the characteristic 
lines of the gas in the tube. 

Geissler tubes often ex¬ 
hibit stratifications , which 
consist of portions of 
greater brightness sepa¬ 
rated by darker intervals. Stratifications have been 
produced throughout a tube 50 feet long. These stratifi¬ 
cations or strise present an unstable flickering motion, re¬ 
sembling that sometimes observed during auroral displays. 







Figure 435. — Geissler Tubes. 


507. The Discharge Intermittent. — On a disk of white card¬ 
board about 20 cm. in diameter paste disks of black paper 2 cm. in 

diameter (Fig. 436). Rotate the disk 
rapidly by means of a whirling table or 
an electric motor and illuminate it by a 
Geissler tube in a dark room. The black 
spots will be sharp in outline because 
each flash is nearly instantaneous; and 
the spots in the different circles will 
either stand still, rotate forward, or rotate 
backward. If in the brief interval be¬ 
tween the flashes the disk rotates through 
an angle equal to that between the spots 
in one of the circles, the spots will appear 
to stand still; if it rotates through a 
slightly greater angle, the spots will appear to move slowly forward; 
if through a smaller angle, they will appear to move slowly backward. 



Figure 436. — Disk for In¬ 
termittent Illumination. 












412 


ELECTROMAGNETIC INDUCTION 




Mount a Geissler tube on a frame attached to the axle of a small 
electric motor (Fig. 437). Illuminate the tube by an induction coil 
while it rotates. Star-shaped figures will 
be seen, consisting of a number of images 
of the tube, the number depending on the 
speed of the motor as compared with the 
period of vibration of the circuit breaker. 

508. Cathode Rays. — When the 
gas pressure in a tube is reduced 
below about a millionth of an atmos¬ 
phere, the character of the discharge 
is much altered. The positive 
column of light extending out from 
the anode gradually disappears, and 
the sides of the tube glow with 
brilliant phosphorescence. With 
English glass the glow is blue ; with 
German glass it is a soft emerald. 
The luminosity of the glass is produced by a radiation in 
straight lines from the cathode of the tube; this radiation 
is known as cathode rays. They were first studied by 
Sir William Crookes, 
and the tubes for the 
purpose are called 
Crookes tubes. 


Figure 437. — Rotation 
of Geissler Tube. 


Many other substances 
besides glass are caused to 
glow by the impact of cath¬ 
ode rays (Fig. 438), such 
as ruby, diamond, and va¬ 
rious sulphides. The color 
of the glow depends on the 
substance. 

Cathode rays have a mechanical effect. In fact they consist of. 
electrons (§ 518) moving w\th very high velocity approaching that 


Figure 438. — Fluorescence by Cathode 
Rays. 



Sir William Crookes, a dis¬ 
tinguished English chemist, 
was born in 1832. In 1873 
he began a series of investi¬ 
gations on the properties of 
high vacua. While engaged 
in this work he invented the 
radiometer, developed the 
Crookes tubes, and dis¬ 
covered what he called “ra¬ 
diant matter.” His investi¬ 
gations led him very close to 
the discoveries of Rontgen. 
He edited the Quarterly Jour¬ 
nal of Science from 1864 until 
his death in 1919. 


Wilhelm Konrad Rontgen 

was born in 1845. It was 
at Wurzburg, Germany, in 
1895, that he discovered 
while passing electric charges 
through a Crookes tube, that 
a certain kind of radiation 
was emitted capable of pass¬ 
ing through many substances 
known to be opaque to light. 
The nature of these rays 
being unknown, he called 
them “ X-rays.” They differ 
from the cathode rays dis¬ 
covered by Crookes, in that 
they affect a sensitized photo¬ 
graphic plate. 












; • ' ' ' 

















































• j • 















































































CATHODE RATS 


413 


of light. When they strike 
a target, their motion is 
arrested and their energy 
of motion is largely trans¬ 
ferred to the target. The 



Figure 439. — Railway Tube. 


light paddle wheel in Figure 439 runs smoothly on glass rails. It may 



Figure 440. — Magnetic Deflection of Cathode Rays. 



be made to traverse the tube in either direction by projecting elec¬ 
trons from the cathode against the 
paddles on top. When the cathode 
is changed from one end to the 
other by reversing the current in 
the induction coil, the little wheel 
stops promptly and reverses its di¬ 
rection. Its paddles are driven as 
if by a blast from the cathode disk. 

Cathode rays, unlike rays of light, 
are deflected by a magnet, and when 
once deflected they do not regain 
their former direction (Fig. 440). 
Cathode rays proceed in straight 
lines, except as they are deflected 
by a magnet or by mutual repul¬ 
sion. A screen placed across their 
path interrupts them and casts a 
shadow on the walls of the tube. 

When the cathode is made in the 
form of a concave cup, the rays are 
Figure 441. — Focus Tube. brought to a focus near its center of 












414 


ELECTROMAGNETIC INDUCTION 


curvature; platinum foil placed at this focus is raised to bright 
incandescence and may be fused (Fig. 441). Glass on which an 
energetic cathode stream falls may be heated to the point of fusion. 

It has been conclusively shown that cathode rays carry 
negative charges of electricity. Hence the mutual repul¬ 
sion exerted on each other by two parallel cathode streams. 

509. Roentgen Rays. — The rays of radiant matter, as 
Crookes called it, emanating from the cathode, give rise to 
another kind of rays when they strike the walls of the 
tube, or a piece of platinum placed in their path. These 
last rays, to which Roentgen, their discoverer, gave the 

name of “ X-rays ,” 
can pass through 
glass, and so get 
out of the tube. 
They also pass 
through wood, 
paper, flesh, and 

Figure 442. — Roentgen Tube. many other sub¬ 

stances opaque to 

light. They are stopped by bones, metals (except in very 
thin sheets), and by some other substances. Roentgen 
discovered that they affect a photographic plate like light. 
Hence, photographs can be taken of objects which are 
entirely invisible to the eye, such as the bones in a living 
body, or bullets embedded in the flesh. 

A Crookes tube adapted to the production of Roentgen 
rays (Fig. 442) has a concave cathode K\ and at its focus 
an inclined piece of platinum A , which serves as the anode. 
The X-rays originate at A and issue from the side of the 
tube. 

510. X-Ray Pictures. — The penetrating power of Roentgen rays 
depends largely on the pressure within the tube. With high exhaus- 





THE FLUOROSCOPE 


415 


tion the rays have high penetrating power and are then known as 
“ hard rays.” Hard rays can readily penetrate several centimeters of 
wood, and even a few millimeters of lead. With somewhat lower 
exhaustion, the rays are 
less penetrating and are 
then known as “ soft rays.” 

The possibility of X-ray 
photographs depends on 
the variation in the pene¬ 
trability of different sub¬ 
stances for X-rays. Thus, 
the bones of the body ab¬ 
sorb Roentgen rays more 
than the flesh, or are less 
penetrable by them. 

Hence fewer rays traverse 
them. Since Roentgen 
rays cannot be focused, all 
photographs taken by them 
are only shadow pictures. 

A Roentgen photograph of 
a gloved hand is shown in 
Figure 443. The ring on 
the little finger, and the 
cuff studs are conspicu¬ 
ous. The flesh is scarcely 
visible because of the high 
penetratiug power of the rays used. The photographic plate for the 
purpose is inclosed in an ordinary plate holder and the hand is laid 
on the holder next to the sensitized side. 

511. The Fluoroscope. — Soon after the discovery of 
X-rays it was found that certain fluorescent substances, 
like platino-barium-cyanide, and calcium tungstate, be¬ 
come luminous under the action of X-rays. This fact 
has been turned to account in the construction of n fluoro¬ 
scope (Fig. 444), by means of which shadow pictures of 
concealed objects become visible. An opaque screen is 




416 


ELECTROMAGNETIC INDUCTION 


covered on one side with the fluorescent substance; this 
screen fits into the larger end of a box blackened inside, 

and having at the other end 
an opening adapted to fit 
closely around the eyes, so 
as to exclude all outside 
light. When an object, such 
as the hand, is held against 
the fluorescent screen and 
the fluoroscope is turned 
Figure 444. — Fluoroscope. toward the Roentgen tube, 

the bones are plainly visible 
as darker objects than the flesh because they are more 
opaque to X-rays. The beating heart may be made visible 
in a similar manner. 

IV. RADIOACTIVITY AND ELECTRONS 

512. Radioactivity. — Wrap a photographic plate in black paper. 
Flatten a Welsbach mantle and lay it on the paper next to the film 
side of the plate. Place the whole in a light-tight box for about a 
week. If the plate be now developed, a photographic picture of the 
mantle will appear on it. 

The mantle contains the rare metal thorium. This 
metal possesses the property of emitting all the time 
radiations that act like X-rays on a photographic plate. 
Substances having this property are known as radioactive. 
The principal ones are uranium, polonium, actinium, tho¬ 
rium, radium, and their compounds. 

513. Discovery of Radioactivity. —The activity of X-rays 
in producing photographic changes led directly to the dis¬ 
covery of the radioactivity of uranium by Becquerel in 
1896. He found that uranium salts give off spontaneously 
radiations capable of passing through black paper and thin 



THREE KINDS OF RADIUM RAYS 


417 


sheets of aluminum foil, and that they affect photographic 
plates as X-rays do. These radiations are not modified in 
any way by the most drastic treatment of the uranium, 
whether by heat or cold or other physical changes. 

514. Radium. — Two years after Becquerel’s discovery 
Madame Curie found in pitchblende (an impure oxide of 
uranium) a constituent much more highly radioactive than 
uranium itself. She succeeded by chemical means in ex¬ 
tracting this remarkable substance from pitchblende and 
named it radium. 

Radium is a million times more radioactive than ura¬ 
nium. Although widely distributed, the total quantity of 
radium in the earth is undoubtedly small. It takes 150 
tons of pitchblende to furnish one ounce of radium. It is 
a hard white metal, resembling barium. It is very un¬ 
stable and is usually prepared and used as a chloride or a 
bromide. Its radiations excite strong fluorescence in 
several substances, notably zinc sulphate, diamond, and 
ruby; and they produce on the 
human body sores difficult to heal. 

515. Three Kinds of Radium Rays. — 

Rutherford has shown that radium 
emits three kinds of “rays,” which 
can be separated by means of a strong 
magnetic field. Their difference in 
behavior in a magnetic field is illus¬ 
trated in Figure 445. The radium is 
placed at the bottom of a small hole 
in a block of lead, so that only a thin 
pencil of rays escapes in a vertical 
direction. A strong magnetic field is applied so that the 
lines of force run away from the observer. The radiations 
are then separated into three kinds, known as alpha , beta, 



Figure 445. — Alpha, 
Beta, and Gamma Rays. 






418 


ELECTR O MA GNETIC 1ND UCTION 


and gamma rays. The alpha rays are slightly deflected 
to the left, the beta rays strongly to the right, while the 
gamma rays are not affected in the least. The fact that 
the alpha and beta rays suffer deviations in opposite direc¬ 
tions shows not only that they are charged particles, but 
that they are oppositely charged, the former positively 
and the latter negatively. 

The alpha rays are positively charged particles emitted 
with an average velocity about one-fifteenth the speed of 
light. They have little penetrating power and are ab¬ 
sorbed by a sheet of ordinary writing paper. 

The beta rays are negatively electrified, highly penetra¬ 
tive, and identical in nature with cathode rays (§ 508). 
They travel with an average speed from about one-half 
down to about one-tenth that of light. 

The gamma rays are of very high penetrating power, they 
travel with the velocity of light, and appear to be identical 
with X-rays. They show no trace of electrification. 

516. Radium a Product of Disintegration.—Uranium has 
the highest atomic weight of any known substance, and it 
is always associated in nature with other radioactive sub¬ 
stances. This association suggested that the other radio¬ 
active substances are derived from uranium by its dis¬ 
integration, or loss of particles with reduction of atomic 
weight. Such has been found to be the case. Uranium 
is the parent of ionium, and ionium is the parent of radium. 
Radium is thus a product of disintegration. 

Further, the radium atom disintegrates with the expul¬ 
sion of an alpha particle ; and the alpha particle, after losing 
its positive charge, becomes an atom of helium. Thus a 
known element is produced during the transformation of 
radioactive matter. All alpha particles from whatever 
source consist of helium atoms carrying positive charges. 



Madame Marie Sklodowska Curie was born in Warsaw in 
1867. She imbibed the spirit of scientific research from her 
father, a distinguished physicist and chemist. In 1895 she mar¬ 
ried Professor Curie of the University of Paris. Three times she 
has been awarded the Gegner prize by the French Academy for 
her valuable contributions to the world’s knowledge of the mag¬ 
netic properties of iron and steel and for her discoveries in radio¬ 
activity. In 1903 and again in 1911 the Nobel prize was awarded 
her. In January of 1911 she failed only by two votes of election 
to membership in the French Academy of Sciences, being de¬ 
feated by Branley, the inventor of the coherer used in the Mar¬ 
coni system of wireless telegraphy. 





Sir Joseph John Thomson was born near Manchester, Eng¬ 
land, in 1856. He received his early training at Owens College, 
and acquired there some knowledge of experimental work in the 
laboratory of Balfour Stewart. At the age of twenty-seven he 
was appointed to the Cavendish professorship at the University of 
Cambridge, a position made famous by Maxwell and Rayleigh. 
The wisdom of the appointment was soon proved; for shortly 
after, Thomson began a series of experiments on the conduction 
of electricity through gases, culminating in the discovery of the 
“ electron,” out of which has developed the electron theory of 


matter. 





ELECTRONS 


419 


Evidence derived from the study of uranium minerals 
makes it almost certain that the final product of the dis¬ 
integration of uranium is lead. 

517. Heat Generated by Radium.—The salts of radium 
exhibit an altogether new and remarkable property ; they 
are always maintained at a temperature several degrees 
higher than that of the surrounding air. They are thus 
always radiating heat and giving out energy. A gram of 
pure radium would emit heat at the rate of from 100 to 
130 calories per hour. It has been estimated that before 
a gram of radium is exhausted it would emit enough heat 
to melt a*gram of ice every hour for 1000 years. Also, 
that the energy of radium is a million and a half times 
greater than that of an equal mass of coal. 

518. Electrons. — Sir William Crookes, at the time of his 
discovery of the cathode discharge, regarded it as matter 
in a radiant state. Later it was demonstrated that the 
cathode discharge carries negative electricity. Still later, 
by a series of brilliant experiments, Sir J. J. Thomson 
proved that cathode “rays” consist of streams of negatively 
electrified particles, now called electrons. The mass of an 
electron is only about y-gVo of the mass of the hydrogen 
atom. Moreover, he measured their speed in a vacuum 
and found it to have the enormous value of about 50,000 
miles per second. 

The electron is invariable in magnitude, and is said to 
be “ the atom of electricity,” that is, the smallest quantity 
of electricity that can be transferred from one atom of 
matter to another. It is the smallest quantity that exists 
in a separate state. 

The beta rays spontaneously emitted by radium and other 
radioactive matter have now been identified with the elec¬ 
trons of a Crookes tube. There is good evidence also that 


420 


ELECTROMAGNETIC INDUCTION 


the electron is identical with the single atomic charge of 
a negative ion in electrolysis. If positive electricity is 
atomic, its atom is several thousands of times greater than 
the atomic quantity of negative electricity. 

Electrons enter into the composition of all matter. An 
electric current is supposed to be a stream of electrons 
flowing under electric pressure through a conductor from 
negative to positive. 


CHAPTER XIV 


DYNAMO-ELECTRIC MACHINERY 
I. DIRECT CURRENT MACHINES 

519. A Dynamo-Electric Generator is a machine to convert 
mechanical energy into the energy of currents of electric¬ 
ity. It is a direct outgrowth of the brilliant discoveries 
of Faraday about induced electromotive forces and currents 
in 1881. It is an essential part of every system, steam or 
hydro-electric, for electric lighting, the transmission of 
electric power, electric railways, electric locomotives, elec¬ 
tric train lighting, the charging of storage batteries, electric 
smelting, electrolytic refinement of metals, and for every 
other purpose to which large electric currents are applied. 

520. Essential Parts of a Dynamo-Electric Machine. — Every 
dynamo-electric machine has three essential parts: 1. The 
field magnet to produce a powerful magnetic field. 2. The 
armature , a system of conductors wound on an iron core, 
and revolving in the magnetic field in such a manner that 
the magnetic flux through these conductors varies con¬ 
tinuously. 8. The commutator, or the collecting rings and 
the brushes, by means of which the machine is connected 
to the external circuit. If the magnetic field is produced 
by a permanent magnet, the machine is called a magneto , 
such as is used in an automobile for ignition; if by an 
electromagnet, the machine is a dynamo, which is used in 
electric lighting stations, and for all other purposes requir¬ 
ing large currents generated by high power. Both are 
often called generators. 


421 


422 


DYNAMO-ELECTRIC MACHINERY 



Figure 446. — Ideal Simple Dynamo. 


521. Ideal Simple Dynamo. —For the purpose of simpli¬ 
fying what goes on in the revolving coils of a generator, 
let us consider a single loop of wire revolving between the 
poles of a magnet (Fig. 446) in the direction of the arrow 

and around a horizontal 
axis. The light lines 
indicate the magnet flux 
running across from N 
to S. In the position of 
the loop drawn in full 
lines it incloses the 
largest possible magnetic 
flux or lines of force, but as the flux inclosed by the coil 
is not changing, the induced E.M.F. is zero. 

When it has rotated forward a quarter of a turn, its 
plane will be parallel to the magnetic flux, and no lines 
of force will then pass through it. During this quarter 
turn the decrease in the magnetic flux, threading through 
the loop, generates a direct E.M.F.; and if the rotation 
is uniform, the rate of decrease of flux through the loop 
increases all the way from the first position to the one 
shown by the dotted lines, where it is a maximum. The 
arrows on the loop show the direction of the E.M.F. 

During the next quarter turn there is an increase of 
flux through the loop, but it runs through the loop in 
the opposite direction because the loop has turned over; 
this is equivalent to a continuous decrease in the original 
direction, and therefore the direction of the induced 
E.M.F. around the loop remains the same for the entire 
half turn; the E.M.F. again becomes zero when the 
half turn is completed. 

After the half turn, the conditions are all reversed and 
the E. M. F. is directed the other way around the loop. 



















THE COMMUTATOR 


423 


If there are several turns in the coil, the E. M. F. reverses 
in all of them twice every revolution. 

The curve of Figure 447 shows by its ordinates the suc¬ 
cessive relative values of the induced electromotive forces 
when the coil rotates 
with uniform speed. If 
the coil is part of a 
closed circuit, the cur¬ 
rent through it reverses 
twice every revolution, 
that is, it is an alternat¬ 
ing current. 

522. The Commutator. — When it is desired to convert 
the alternating currents flowing in the armature into a 
current in one direction through the external circuit, a 
special device called a commutator is employed. For a 
single coil in the armature, the commutator consists of two 
parts only. It is a split tube with the two halves, a and £>, 
insulated from each other and from the shaft 8 on which 
they are mounted (Fig. 448). The two ends of the coil 

(not shown) are connected 
with the two halves of the 
tube. 

Two brushes, with which 
the external circuit L L is 
connected, bear on the com¬ 
mutator, and they are so 
placed that they exchange 
contact with the two commu¬ 
tator segments at the same time that the current reverses 
in the coil. In this way one of the brushes is always 
positive and the other negative, and the current flows in 
the external circuit from the positive brush back to the 



Figure 448. — Two-part Commu¬ 
tator. 



Figure 447. — Curve of E. M. F.’s. 





























424 


DYNAMO-ELECTRIC MACHINERY 



Figure 449. — Rectified E. M. F.’s. 


negative, and thence through the armature to the positive 
again; but with a single coil the current is pulsating, or 

falls to zero twice every 
revolution (Fig. 449). 

523. The Gramme Ring. 
— The use of a commu¬ 
tator with more than 
two parts is conven¬ 
iently illustrated in 
connection with the 
Gramme ring. This ar¬ 
mature has gone out of practical use, but it is useful here 
because it can be understood from a simple diagram; and 
fundamentally its action is the same as that of the com¬ 
mon drum type. 

The Gramme ring has a core made either of iron wire, 
or of thin disks at right angles to the axis of rotation. 
The iron is divided for the purpose of preventing induc¬ 
tion or eddy currents in it, which waste energy. The re¬ 
lation of the several parts of the machine is illustrated by 
Figure 450. A number of coils are wound in one direction 
and are all joined in series. The coils must be grouped 
symmetrically so that some 
of them are always active, 
thus generating a continuous 
current. Each junction be 
tween coils is connected with 
a commutator bar. Most of 
the magnetic flux passes 
through the iron ring from 



Figure 450. — The Gramme Ring. 


the north pole side to the south pole; hence, when a coil 
is in the highest position in the figure, the maximum flux 
passes through it, as the ring rotates, the flux through the 






























THE FIELD MAGNET 


425 


coil decreases, and after a quarter of a revolution there is 
no flux through it. The current through each coil reverses 
twice during each revolution, exactly as in the case of the 
single loop. No current flows entirely around the arma¬ 
ture, because the E.M.F. generated in one coil at any in¬ 
stant is exactly counterbalanced by the F.M.F. generated in 
the coil opposite. But when the external circuit connect¬ 
ing the brushes is closed, a current flows up on both sides 
of the armature. The current has then two paths through 
the armature, and one brush is constantly positive and the 
other negative. The current is therefore direct and fairly 
steady. 

524. The Drum Armature. — This very 
useful form of armature is in universal 
use for direct current (D. C.) genera¬ 
tors. The core is made up of thin iron 
disks stamped out with teeth around 
the periphery (Fig. 451). When these 
are assembled on the shaft, the slots ^qothed^Disk"" 
form grooves in which are placed the 

armature windings. All the coils in the armature may be 
joined in series, and the junctions between them are con¬ 
nected to the commutator bars, as in the Gramme ring. 

525. The Field Magnet. — The magnetic field in dynamos 
is produced by a large electromagnet excited by the cur¬ 
rent flowing from the armature , this current is led, either 
wholly or in part, around the field-magnet cores. When 
the entire current is carried around the coils of the field 
magnet, the dynamo is said to be series wound (Fig. 
452 a). When the field magnet is excited by coils of 
many turns of fine wire connected as a shunt to the exter¬ 
nal circuit, the dynamo is said to be shunt wound (Fig. 
452 5). A combination of these two methods of exciting 



426 


DYNAMO-ELECTRIC MACHINERY 


the field magnet is called compound winding (Fig. 452 c ). 
The residual magnetism remaining in the cores is suffi¬ 
cient to start the machine. The current thus produced 



Figure 452. — Field Magnet Windings. 


increases the magnetic flux through the armature and so 
increases the E.M.F. 

526. The Modern Generator. — Large modern D. C. gen¬ 
erators are multipolar, with four, six, or eight, or more 
poles. The larger number of poles reduces the rate of 
rotation of the armature. In the field magnet shown in 
the half tone on the opposite page there are sixteen poles, 
north poles and south poles alternating around the ring. 
The armature is wound in loops which reach across a 
chord nearly equal to the pitch of the poles, so that when 
one side of a loop is passing a north pole, the opposite 
side is passing an adjacent south pole. In a simple drum 
armature there are as many brushes as there are field 
poles, and there are the same number of parallel paths or 
circuits through the windings as there are brushes. An 
engine type of multipolar drum armature is shown in the 
illustration on the opposite page. 

527. The Electric Motor. —The electric motor is a machine 
for the conversion of the energy of electric currents into 
mechanical power. 

















































Field Magnet of D. C. Generator. Drum Armature of D. C. Generator. 











































* 




































THE ELECTRIC MOTOR 


427 


In the electric automobile and in the electric starter for gasoline 
machines the motor is driven by currents from a storage battery. In 
the electric street car it derives its current and power from a trolley, 
a third rail, or from conductors fixed in a slotted conduit under the 
pavement, all of them leading back to a power house or a substation. 
The electric motor is extensively used for small power as well as for 
large units. Witness the use of electric fans, electric coffee grinders, 
sewing machine motors, and electrically driven bellows for pipe organs 
on one hand, and on the other the electric drive for large fans to ven¬ 
tilate mines and buildings, electric elevators, and electrically driven 
mills and factories. 

An electric motor for direct currents is constructed in 
the same manner as a generator. In fact, any direct cur¬ 
rent generator may be used as a motor. A study of the 
magnetic field resulting from the interaction of the field 
due to the field magnet and that of a single loop carrying 
an electric current will make 
it clear that such a loop has 
a tendency to rotate. 

Figure 453 was made from 
a photograph of the field 
shown by fine iron filings 
between unlike poles. This 
field is distorted by a current 
through a loop of wire, which 
came up through the hole on 
the right in the glass plate and went down through the other. 
Many of the lines of force are threaded through the wire 
loop instead of running directly across from one magnetic 
pole to the other. Now the lines of magnetic force are 
under tension and tend to straighten out; this straight¬ 
ening brings a magnetic stress to bear on the loop carrying 
the current and tends to turn it counter-clockwise in the 
case shown in the figure. 



Figure 453. — Magnetic Field 
Distorted by Current. 






428 


D YNAMO-ELECTRIC MA CHINER Y 


If the loop be allowed to rotate in the direction of this 
magnetic effort between the field and the loop, the loop 
will become the armature of a motor and work will be 
done by the machine at the expense of the energy of the 
current flowing through it. If, however, the loop be 
forcibly rotated clockwise by mechanical means, it will 
turn against the magnetic effort acting on it, and work 
will be done against the resistance of this magnetic 
drag. The loop will then be the armature wire of a 
generator. 

528. Forms of D. C. Motors. — Since any D. C. generator 
will run as a motor, we find D. C. motors either series or 
shunt wound according to the service for which they are 
designed. Series wound motors are used on street cars and 
electric automobiles, where the service requires variable 
speed. Shunt wound motors are used to run machinery in 
shops and factories, where constant speed is desirable. 
High speed motors are usually bipolar; motors for slow 
speed service have multipolar fields. 

The torque, or turning moment, of an electric motor 
depends both upon the strength of the magnetic field 
and the current through the armature. In a shunt 
wound motor the field strength is nearly constant; 
hence the torque varies directly as the current through 
the armature. In a series motor, on the other hand, 
the strength of field varies nearly as the current, and 
the current is the same through the field and the arma¬ 
ture. Hence the torque varies as the square of the cur¬ 
rent. If the current is doubled, it is doubled in both 
the field and the armature, and the torque is therefore 
quadrupled. The series motor is accordingly used where 
a large starting torque is required, as in cranes and motor 
vehicles. 


STARTING RESISTANCE 


429 


529. Back E. M. F. in a Motor. — Connect an incandescent 
lamp on the lighting circuit in series with a small motor. Clamp the 
armature or hold it stationary, and turn on the current. The lamp 
will glow with full brilliancy. Next let the motor run at full speed 
without load; the lamp will now grow dim. 

If the motor is provided with a flywheel to keep up its motion 
when the current is shut off, the lamp and the motor may be con¬ 
nected to the mains in parallel. Then when the motor is running at 
full speed, the lamp will glow with nearly or quite normal brilliancy. 
Now open the switch, cutting off both the lamp and the motor from 
the mains; the lamp will glow for a few seconds nearly as brightly 
as before the main circuit was opened. 

The first experiment shows that the motor running 
takes less current than when the armature is held fast. 
But since the resistance in circuit remains unchanged, 
the lessened current by Ohm’s law must be ascribed to a 
smaller E.M.F. The fact is, the motor produces a back 
E.M.F. nearly equal to the applied E.M.F. Denote the 
back E.M.F. by E' ; then by Ohm’s law 

t E-E ' 

R * 

Since the current is small when the motor is running. 
E’ must be nearly equal to E. 

The second experiment shows the back E.M.F. directly, 
for it lights the lamp so long as the motor is kept running 
by the energy stored in the flywheel after shutting off 
both the lamp and the motor from the supply mains. The 
armature revolves in a magnetic field and generates an 
E.M.F. for the same reason that it does when spun as a 
generator. 

530. Starting Resistance. — The resistance of a motor 
armature is small, and a motor at rest has no back 
E.M.F. to limit the current. If therefore the current 
were turned on without temporary starting resistance in 



430 


D YNA MO-EL EC TRIC MA CHINER Y 


circuit, there would be a great rush of current, which 
might damage the motor, blow the line fuses, and possibly 
throw open the automatic circuit breaker in the power 
house. Hence the use of a starter, which is a rheostat 

with a number of graduated 
resistances (Fig. 454). 
When the switch arm is 
turned to touch the first live 
contact point, the circuit is 
closed through enough re¬ 
sistance to avoid danger. 
As the motor speeds up and 
generates larger and larger 
back E.M.F., the resist¬ 
ance is gradually cut out 
by moving the switch arm 
to successive contact points, 
until the starting resistance 
is all out and the motor is 
running at full speed. In the figure A is the armature 
and F the field coil of a shunt motor. 

The switch arm is often held in place by a release 
magnet M after the entire starting resistance is cut out. 
If the line switch is opened, or the circuit broken in any 
other way, the magnet releases the arm and a spring 
throws it back to open circuit. This prevents injury if 
the current should suddenly come on again. 

531. Electric Railways. —The electric current is usually 
conveyed to the moving car by trolley wire, a third rail, or 
by a conductor laid in a slot-conduit between the rails. 
Direct current under an electric pressure of 550 volts is 
nearly always used. A feeder wire is often employed to 
prevent too great a drop in voltage at distant points 



Figure 454. — Starting Resistance 
for Motor. 



























Electric Engine Crossing the Rockies on a Two Per Cent Grade. 


















Armature Core of A. C. Generator. Field Magnet of A. C. Genera:or. 








THE ALTERNATOR 


431 


(Fig. 455). The circuit is from the positive brush of 
the generator to the feeder and trolley wires or third rail, 
thence through the motors to the car wheels and track, 
and so back to the negative terminal of the generator. 

Each car is equipped with two series wound, four- 
pole motors. They drive the wheels through a single 
reduction gear. At starting, the “ controller ” or start- 


Feeder Wire 



Rails 

Figure 455. — Electric Railway and Feeder. 


ing rheostat places the two motors in series with some 
resistance. After the car has started, this resistance is 
first cut out; then the motors are joined in parallel with 
resistance in circuit; this resistance is finally cut out 
after the car attains sufficient speed. As the motor 
speeds up it generates a back-electromotive force, which 
reduces the current to its working value. 

II. ALTERNATORS AND TRANSFORMERS 

532. The Alternator. — If the ends of the armature coil 
are connected to two slip-rings (Fig. 456) by which slid¬ 
ing contact is made with the 
brushes A and B and the external 
circuit, the machine becomes an 
alternator , and the current flowing 
in the external circuit CD will 
alternate or reverse, as it does 

Figure 456. — Slip-rings. 

in an armature coil, every time 

the armature turns through the angular distance from one 
pole to the next. 






































432 


DYNAMO-ELECTRIC MACHINERY 


A complete series of changes in the current and E.M.F. 
in both directions takes place while the armature is turn¬ 
ing from one pole to the next one of the same name. 
Such a series of changes is called a cycle . The frequency, 
or the number of cycles per second, is equal to the product 
of the number of pairs of poles on the field magnet and 

the number of rotations 
per second. Frequencies 
are now restricted be¬ 
tween the limits of about 
25 and 60 cycles per 
second. Multipolar ma¬ 
chines are used to avoid 
excessive speed of rota¬ 
tion. 

Figure 457 is a dia¬ 
grammatic sketch of an 
alternator with a station¬ 
ary field outside and an 
armature rotating with the shaft. The field is excited 
by a small direct current machine called the exciter. The 
armature coils are reversed in winding from one field pole 
N to the next S, they are joined in series, and the termi¬ 
nals are brought out to rings B on the shaft. The 
brushes bearing on these rings lead to the external circuit. 

533. Alternators with Rotating Field. — Since the rotation 
of the armature with respect to the field is only relative, 
it clearly makes no difference in the generation of E.M.F. 
whether the armature or the field is made the rotating 
member. In large alternators (A. C. generators) the 
armature is the stationary member outside and the field 
rotates within. Slow speed generators necessarily have a 
large number of poles. This construction follows the 



Figure 457. — Alternator with Sta¬ 
tionary Field. 






LAG OF CUBE ENT BEHIND E. M. F. 


433 


best engineering practice, since it permits better insula¬ 
tion of the armature windings on the stationary member 
of the machine and avoids the transmission of high volt¬ 
ages by sliding contacts on slip rings. 

The armature core is built up from punchings of 
selected steel of superior magnetic quality; these punch¬ 
ings are coated with insulating varnish to reduce eddy 
current losses. The armature punchings are securely 
bolted together between two cast-iron rings having an 
I-beam section. Air ducts are left in the core for the 
purpose of ventilation. 

534. Lag of Current Behind E.M.F. — When the circuit 
has self-inductance, an alternating E.M.F. produces a 
current which lags behind the E.M.F.; and as a conse¬ 
quence Ohm’s law is no longer adequate to express its 
value. The self-inductance not only introduces an addi¬ 
tional E.M.F., but it causes the current to come to its 
maximum value later than 
the E.M.F. impressed on 
the circuit by the generator. 

Figure 458 is reproduced 
from a photograph made by 
the E.M.F. and currents 
themselves in an instru¬ 
ment called an oscillograph. 

It is a kind of double gal¬ 
vanometer in which the movable systems have so short a 
period that they can follow all the oscillations of the 
current and E.M.F. A beam of light is reflected from 
a tiny mirror in the instrument and acts on a rapidly 
moving photographic plate. E in the figure is the curve 
of the impressed E.M.F. and I that of the current. The 
latter in this case came to its maximum nearly a quarter 



Figure 458. — Lag of Current be¬ 
hind E.M.F. 



434 


DYNAMO-ELECTRIC MACHINERY 



Figure 459. — Two-phase Currents. 


of a period later than the former. (Trace the curves 
from left to right.) 

535. Polyphase Alternators.— Two or more currents of 
the same frequency, but differing in phase (§ 196), may 

be obtained from 
one generator. 
Two-phase or three- 
phase currents are 
specially useful for 
the transmission of 
power and for driv¬ 
ing induction mo¬ 
tors ; at the same 
time they are just 
as useful for lighting purposes as the current from a 
single-phase machine. 

In a two-phase alternator there are two sets of wind¬ 
ings, the one set being displaced from the other by half 
the pole pitch; the two electromotive forces induced in 
them in consequence differ by a quarter of a period 
(Fig. 459). When 
one of these electro¬ 
motive forces passes 
through zero value, 
the other will be at 
its maximum. 

In a three-phase 
alternator there are 
three separate sets of 
windings, displaced 
from one another by two-thirds of the pole pitch. There 
are generated three electromotive forces of equal ampli¬ 
tude, but differing in phase by one-third of a period 



Figure 460.-Three-phase Currents. 













TRANSFORMERS 


435 


(Fig. 460). The three-phase system is best adapted to 
the transmission of power. Three lines only are needed 
instead of six. If one end of each winding is brought 
to a common junction, and the other ends are connected 
respectively to the three lines, no return is needed, since 
each line in succession serves as the return for the other 
two. This may be understood from an examination of 
Figure 460, which shows that the sum of the two currents 
or electromotive forces in one direction at any instant is 
always equal to the third in the other direction; in other 
words, the algebraic sum of the three is always zero. 

536. Transformers. — A transformer is an induction coil 
with a primary of many turns of wire and a secondary of 
a smaller number, both wound around a divided iron core 
forming a closed magnetic circuit; 
that is, one magnetic circuit is in¬ 
terlinked with two electric circuits 
(Fig. 461). A transformer is em¬ 
ployed with alternating currents 
either to step down from a high 
E.M.F. to a low one, or the re¬ 
verse. The two electromotive forces 
are directly proportional to the num¬ 
ber of turns of wire in the two coils. 

For example, to reduce a 2000-volt 
current to a 100-volt current, there 
must be 20 turns in the primary to every one in the sec¬ 
ondary. Both coils are wound on the same iron core, and 
are as perfectly insulated from each other as possible. 
The iron serves as a path for the flux of magnetic induce 
tion, and all the lines of force produced by either coil 
pass through the other, except for a small amount of 
“magnetic leakage.” When the secondary is open, the 



Figure 461. — Trans¬ 
former. 




436 


DYNAMO-ELECTRIC MACHINERY 


transformer acts simply as a “ choke coil ”; that is, the 
self-induction of the primary is so large that only sufficient 
current is transmitted to magnetize the iron and to fur¬ 
nish the small amount of energy lost in it. 

The counter-E.M.F. of self-induction is then nearly 
equal to the E.M,F. impressed from without. But 
when the secondary is closed, the self-induction is sup¬ 
pressed to the extent that the transformer automati¬ 
cally adjusts itself to the condition that the energy 
in the secondary circuit lacks only a few per cent of the 
energy absorbed by the primary from the generator. 

537. Transformers in a Long-distance Circuit. — The utility 
of the transformer lies in its use to secure high voltage 
for transmission and low voltage for lighting and power. 
Only small currents can be transmitted over distances 
exceeding a few hundred feet without excessive heat losses 



• Figure 462. — Transformers on Long-distance Circuit. 


on account of the resistance of the conductors. To trans¬ 
mit power while still keeping the current small, the elec¬ 
tric pressure, that is, the number of volts, must be increased, 
for power transmitted in watts is proportional to the prod¬ 
uct of the number of volts and the number of amperes. 

Figure 462 is a diagram showing a transformer system 
for long-distance power transmission. The first trans¬ 
former A raises the potential difference from 2000 volts 
to 50,000 volts. The long distance transmission takes 
place at this voltage to the second transformer i?, which 
steps down from 50,000 to 2000 volts for local transmis- 












LONG DISTANCE TRANSMISSION OF POWER 437 

sion within the limits of a city or a district. The third 
transformer <7 steps down further from 2000 to 100 volts 
for house service for lighting, fan motors, electric cook¬ 
ing, electric flatirons, etc. 

538. Long Distance Transmission of Power. — Power is now 
transmitted over long distances by means of alternating 
currents of high voltage. The transmission is invariably 



Figure 463. —Cables and Towers of 150,000-Volt Line. 


by three-phase currents over one or two sets of copper or 
aluminum cables, strung on steel towers at a height of 
about 75 feet. These cables run straight from point to 
point over mountains, valleys, and streams. For example, 
the electric power generated by the hydro-electric plants 





438 


D YNA MO—ELECTRIC MA CHINEE Y 


at Niagara Falls is raised by step-up transformers to 
60,000 volts for transmission to distant cities, — Buffalo, 
Rochester, Syracuse, where it is used for street car service, 
for power motors, and for lighting and other domestic 
purposes. 

At Big Creek in the High Sierras in California, water 
power to the extent of 80,000 H. P. is now used for gen¬ 
erating three-phase electric currents ; the voltage is raised 
by step-up transformers to 150,000 for transmission over 
aluminum cables 241 miles to the Eagle Rock transformer 
station. These cables are 0.96 inch in diameter, and are 
strung IT.5 feet apart, on steel towers averaging seven to 
the mile. At present two sets of three-wire cables are in 
use, each set strung on separate towers (Fig. 463). Ulti¬ 
mately there will be three sets for the transmission of 
320,000 H. P. 

At Eagle Rock step-down transformers reduce the elec¬ 
tric pressure to 15,000 volts for transmission over the 
Los Angeles district, and to 60,000 volts for the Riverside 
district and beyond. The latter district adds about 80 
miles to the transmission, making 320 miles as a maximum. 

539. The Rotating Magnetic Field. — It is of first im¬ 
portance to understand how a magnetic field may rotate 
while the coils producing the field stand still; for the 
rotating field, invented by Ferraris and Tesla, is the secret 
of all A. C. induction motors for two- or three-phase 
currents. A simple experiment will help to clear up the 
problem. 

Suspend a heavy ball by a string at least ten feet long and set it 
swinging north and south with an amplitude of a foot or more. At 
the instant when the ball stops at either extremity of its path, strike 
it a blow with a mallet east and west. This blow will cause an east 
and west simple harmonic motion, differing in phase from the north 



Dam and Power House, Great Falls, Montana. 















Huge Transformers and Switches, Morel Substation, 
Chicago, Milwaukee and St. Paul Railway. 















































THE ROTATING MAGNETIC FIELD 


439 


and south one by a quarter of a period. Further, if the blow is de¬ 
livered with the right force, the two simple harmonic motions, com¬ 
bined in the pendulum, will give rise to uniform circular motion of 
the ball. 


This experiment shows that uniform circular motion 
may be produced by combining two simple harmonic 
motions at right angles to each other, of the same period 
and amplitude, and differing in phase by a quarter of a 
period. 

An alternating current in a coil without iron produces 
an alternating magnetic held along the axis of the coil. 
If the current follows the simple harmonic or sine law, 
the magnetic held will follow it 
also. 

Let two like coils be set with 
their axes at right angles (Fig. 

464), and let two-phase currents be 
passed through them, one through 
coil A A and the other through BB. 

Now these two magnetic helds 
produced by the two-phase cur¬ 
rents are similar to the two motions 
of the ball in the pendulum ex¬ 
periment ; and they combine to produce a rotating mag¬ 
netic held near their common center. A small magnetic 
needle mounted there will spin around rapidly. This is 
analogous to the way in which uniform rotary motion 
without dead points may be produced from two oscillatory 
motions by using two cranks at right angles, as in quarter- 
crank engines, the one impulse following the other at one 
fourth of a period. 

The above combination of two coils at right angles is 
suitable for two-phase currents only. Another way to 



Figure 464. — Coils for 
Rotating Field. 











440 


DYNAMO-ELECTRIC MACHINERY 


make a rotating magnetic field is by three-phase currents. 
These differ in phase by one third of a period (or 120°). 
They are analogous to a three-crank engine with the cranks 
set at angular distances of 120°. 

540. Ways of Combining the Circuits. — The coils or cir¬ 
cuits that receive the polyphase currents may be combined 

in several ways. In Figure 465 for a 
two-phase system, the entire ring is 
wound as a closed circuit like a Gramme 
ring, and the four line wires are at¬ 
tached at four equidistant points. In¬ 
stead of this plan, the winding may be 
divided into four separate coils, all 
having corresponding ends connected 
to a common junction, the other four 
ends being joined to the four line 
wires, AA! for one circuit and BB' for the other. 

For a three-phase system Figure 466 shows the mesh or A 
method of connection. Again the three coils may have a 
corresponding end of each connected to 
a common junction, the other ends re¬ 
maining for the three line wires. This 
is known as the star or F'-connection. 

Again, the coils may not be wound 
upon a ring, but on poles projecting in- 
wardo In large multipolar machines 
the three-phase coils may be wound on 
six, nine, or a larger number of poles, 
multiples of three, or they may be embedded in slots as in 
the armature or stator of A. C. generators. 

541. Induction Motors. — In 1888 Ferraris of Italy 
mounted within coils like those of Figure 464 a hollow cop¬ 
per cylinder on pivots at top and bottom. When two-phase 



Figure 466.— 
Winding for Three- 
phase Rotating 
Field. 



Figure 465. —Wind¬ 
ing for Two-phase_Ro- 
tating Field. 





Above: Stator of A. C. Generator Connected to Steam Turbine. 
Below : Field of the Same. 











Above: Stator of Three-phase Motor. 
Below: Three-phase Motor Complete. 









INDUCTION MOTORS 


441 


currents are passed through the two circuits of the Ferra- 
ris apparatus, the copper cylinder is set rotating in the 
direction of the rotating field. The rotation of the field 
causes the lines of force to cut the cylinder and currents 
are induced in the copper. By Lenz’s law (§ 499) the 
cylinder moves in the direction to check the induction in 
it; it is therefore dragged in the same direction as the 
rotation of the magnetic field. The cylinder tends to ro- 



Figure 467 . — Induction Motor with “Squirrel Cage” Rotor. 

tate as fast as the field, but never quite reaches it; for 
then there would be no cutting of lines of force and no 
induction. The difference in speed between the field and 
the rotor, as the cylinder is called, is known as the slip. 
If a little friction is applied to the cylinder, the slip will 
increase until the larger induced currents are just sufficient 
to supply the needed torque. 

In commercial motors the actual rotor consists of a cylin¬ 
drical core built up of thin steel disks, with slots or holes 
through parallel to the shaft. In these are embedded 
heavy copper rods or bars, which are joined together at 















442 


DTNAMO-ELECTRIC MACHINERY 


their ends, so as to form a “squirrel cage” of copper (Fig. 
467). The induced currents flow in the rods. The rotor 
does not need to have either commutator or slip rings 
and is entirely separate from any other circuit. Its cur¬ 
rents are wholly inductive. In some larger forms the 
rotor is wound like a drum armature, and the coils are 
connected through slip-rings, so that resistance may be 
inserted in the circuits at starting. This resistance is cut 
out as the motor gets up its speed. 

III. ELECTRIC LIGHTING 

542. The Carbon Arc. — In 1800 Sir Humphry Davy 
discovered that when two pieces of charcoal, suitably con¬ 
nected to a powerful voltaic battery, were brought into 
contact at their ends and were then separated a slight dis¬ 
tance, brilliant sparks passed between them. No mention 


was made of the electric arc until 



1808. With a battery of 2000 


cells and the carbons in a hori¬ 
zontal line, they could be sepa¬ 
rated several inches, while the 
current was conducted across 
in the form of a curved flame or 
arc. Hence the name electric 
arc given to this form of electric 
lighting. 


Dense compressed or molded 
carbon rods are now used, and 
when they are separated a slight 


Figure 468 . — The Arc Light, 
Direct Current. 


distance they are heated to an exceedingly high tempera¬ 
ture, and the current from a dynamo continues to pass 
across through the heated carbon vapor, which is ionized 
by the emission of electrons from the negative carbon. 



THE OPEN AND THE INCLOSED ARC 


443 


The ends of the carbon rods in the open air are disinte¬ 
grated, a depression or “crater” forming in the positive 
and a cone on the negative (Fig. 468). Most of the light 
of the open arc comes from the bottom of this crater, the 
temperature of which Violle has estimated to be 3500° C. 
The arc light may be produced in a vacuum. The in¬ 
tense heat is not, therefore, generated by combustion. It 
is the energy of the current converted into 
heat by the resistance of the arc. The usual 
current for arc lamps is from 5 to 10 amperes. 

For searchlights, arc lights of great power 
are produced by the use of thicker carbons 
and 100 or more amperes. 

543. The Open and the Inclosed Arc. — To 
keep the carbon rods from burning away too 
rapidly, modern arc lamps are mostly of the 
“ inclosed arc ” type. The lower carbon and 
a part of the upper one are inclosed in a 
small glass globe, which is air-tight at the 
bottom, but allows the upper carbon to slip closed"Arc." 
through a check-valve at the top (Fig. 469). 

Soon after the arc begins to burn, the oxygen in the globe 
is absorbed and the arc is then inclosed in an atmosphere 
of nitrogen from the air and of carbon monoxide from 
the incomplete combustion of the carbon. The inclosed 
arc is longer than the open arc, and the E.M.F. is about 
80 volts instead of 50 as required by the open arc; but 
the current for the inclosed arc is smaller than for the 
open arc. The carbons for the inclosed arc last at least 
ten times as long as in the open air. 

The direct current inclosed arc is operated at a higher 
temperature than the alternating current lamp, and is 
therefore more efficient. 










444 


DYNAMO-ELECTRIC MACHINERY 


544. Other Arc Lights. — Other arc lamps are now in 
commercial use in which the light comes chiefly from the 
incandescent stream between the electrodes. They have 
a higher efficiency than the carbon arc. In the metallic 
arc powdered magnetite in an iron tube is used for one 
electrode and a block of copper for the other. The arc 
flame is very white and brilliant, the light coming from 
the luminous iron vapor. 

Flaming arcs are made by the use of a positive electrode 
impregnated with salts of calcium, chiefly calcium fluoride. 
The light from the flaming arc is yellow, and is adapted 
to outdoor illumination only. 

The mercury arc of Cooper Hewitt is radically different 
from other arc lamps. It has the arc in a sealed tube, 
which is exhausted of air, and the light comes from lumi¬ 
nous mercury vapor. It consists of a glass tube one inch 
in diameter and from 20 to 50 inches long, with a bulb at 
one end for holding mercury, and a small iron electrode at 
the other. A special device must be used to start the 
current. This light contains no red 
rays and thus gives a peculiar color to 
objects illuminated by it. This lamp 
operates by direct current only. 

545. Carbon Filament Lamps. — The 
principle of the incandescent lamp is 
the use of a filament or wire of such 
highresistance that it can be brought 
to glow % the passage of an electric 
current. The filament is inclosed in a 
glass bulb, exhausted of air, and has its ends connected 
thr ough t he glass h^short^pieces of platinum"wire^(Fig. 
470). The carbon filament is myW”TnaHe^oiir^cellulose 
obtained from cotton. 



Figure 470 . — Car¬ 
bon Filament Lamp. 


METAL FILAMENT LAMPS 


445 


The temperature to which a carbon filament can be raised 
is limited by the tendency of the carbon to vaporize at high 
temperatures. The carbon thrown off rapidly reduces the 
thickness of the filament and blackens the globe. The 
useful life of a carbon filament is from 500 to 700 hours. 

The ordinary commercial unib for the carbon filament is 
the l fi-candle-powe r lamp. On a 110-v olt circuit it takes 
about OJi amppirfi. Since the power in watts consumed is 
jST, this lamp requires abo ut 55 watts, or ,3.5 wa tts per 
candle. The efficiency of a lamp is expressed in watts per 
candle. The efficiency of the carbon filament lamp is from 
3.1 to 3.5 watts per candle. 

A metallized filament is obtained by heating a treated 
cellulose filament in an electric furnace to a very high 
temperature. It can be glowed at a higher 
temperature than the ordinary carbon fila¬ 
ment ; it has a corresponding higher ef¬ 
ficiency of about 2.5 watts per candle for 
50 and 60 watt lamps. 

54(T'TSretal Filament Lamps. — Metal wires 
cannot be used in glow lamps unless their 
melting point is higher than that of plati¬ 
num. The melting point of platinum is 
about 1775° and that of tungsten about 
3200° C. The available metals for incan¬ 
descent lamps are tantalum and tungsten. Their specific 
resistance is lower than that of carbon ; hence filaments 
made of them must be longer and thinner than those of 
carbon. A piece of tungsten as large as a lead pencil 
contains enough material to make about five miles of wire 
for 40 watt lamps. A continuous tungsten filament is so 
long that it must be wound zigzag on a light frame or reel 
(Fig. 471). The tungsten 25 watt lamp gives 20 candle 



Figure 471 .— 
Tungsten Fila¬ 
ment Lamp. 







446 


DYNAMO-ELECTRIC MACHINERY 


power, or 1.25 watts per candle. By reason of its high 
efficiency it has largely displaced the carbon lamp, in spite 
of the fact that it is more fragile. The tungsten lamp 
has a useful life of from 800 to 1000 hours. 

547. Gas-filled Lamps. — In many early lamp experi¬ 
ments the glass bulbs, after exhaustion of air, were filled 
with an inert gas. This practice was soon abandoned be¬ 
cause the efficiency was lowered by the heat 
carried away from the filament to the bulb 
by convection in the gas. In recent develop¬ 
ments it has been found that gas can be used 
to advantage with filaments of large cross- 
section in high power lamps. When the bulb 
of a lamp taking more than 75 watts is filled 
with an inert gas, like nitrogen or argon, it 
is possible to raise the temperature of the 

filament and in this way to get a higher efficiency. In 
thicker filaments the loss of heat by convection is more 
than offset by the gain secured by the use of a higher 
temperature. The twenty ampere series lamp, filled with 
argon, has an efficiency of half a watt per candle. In 
other words, a 500 watt lamp has a candle power of 1000. 
These lamps are specially adapted to the lighting of large 
areas and city streets (Fig. 472). 

548. Incandescent Lamp Circuits.—Incandescent lamps 
are connected in parallel between the mains in a building. 



Figure 472 . 
— Gas-filled 
Lamp. 


SB 


o 

O • 

■O 

Figure 473 . — Incandescent 
Lamp Circuit, 


So 


-o- 
o 
-o- 

Figure 474 . — Lamp Circuit with 
Transformer. 












THE TRANSMITTER OR KEY 


447 


These mains lead either directly to a dynamo (Fig. 473), 
or to the low voltage side of a transformer in the case of 
alternating currents (Fig. 474). Single lamps are turned 
off usually by the key in the socket (Fig. 470), and groups 
of lamps by a switch S (Fig. 474). 

IV. THE ELECTRIC TELEGRAPH 

549. The Electric Telegraph is a system of transmitting 
messages by means of simple signals through the agency 
of an electric current. Its essential parts are the line , 
the transmitter or hey , the receiver or sounder, and the 
battery. 

550. The Line is an iron, copper or phosphor-bronze wire, 
insulated from the earth except at its ends, and serving to 
connect the signaling apparatus. The ends of this con¬ 
ductor are connected with large metallic plates, or with 
gas or water pipes, buried in the earth. By this means 
the earth becomes a part of the electric circuit containing 
the signaling apparatus. 

551. The Transmitter or Key (Fig. 475) is merely a cur¬ 
rent interrupter, and usually consists of a brass lever A, 
turning about pivots at B. It 
is connected with the line by 
the screws C and B. When 
the lever is pressed down, a 
platinum point projecting under 
the lever is brought in contact 
with another platinum point 
B, thus closing the circuit. When not in use, the 
circuit is left closed, the switch F being used for that 
purpose. 

552. The Receiver or Sounder (Fig. 476) consists of an 
electromagnet A with a pivoted armature B. When the 



Figure 475 . — Telegraph Key. 



448 


DYNAMO-ELECTRIC MACHINERY 



Figure 476 . —Telegraph Sounder. 


circuit is closed through the terminals D and E, the arma 
ture is attracted to the magnet, producing a sharp click. 

When the circuit is 
broken, a spring C 
causes the lever to rise 
and strike the backstop 
with a lighter click. 

553. The Relay. — 
When the resistance of 
the line is large, the 
current is not likely to 
be strong enough to operate the sounder with sufficient 
energy to render the signals distinctly audible. To 
remedy this defect, an electromagnet, called a relay (Fig. 
477), whose helix A is composed of many turns of fine 
wire, is placed 
in the circuit by 
means of its ter¬ 
minals 0 and D. 

As its armature 
moves to and fro 
between points, 
it opens and 
closes a shorter local circuit through E and F in which 
the sounder is placed. Thus the weak current, through 
the agency of the relay, brings into action a current 
strong enough to work the local sounder with a loud 
click. 

554. The Battery consists of a large number of cells, 
usually of the gravity type, connected in series. It is 
generally divided into two sections, one placed at each 
terminal station, these sections being connected in series 
through the line. The principal circuits of the great 



Figure 477 . — Telegraph Relay. 























Alexander Graham Bell 

was born in Edinburgh, Scot¬ 
land, in 1847. His father, 
Alexander Melville Bell, was 
a teacher and inventor. The 
son came to the United States 
in 1872 and became professor 
at Boston University. While 
there he invented the tele¬ 
phone in 1875. He also in¬ 
vented the photophone, and 
developed his father’s system 
of phonetics. 


Samuel F. B. Morse 

(1791-1872) was born at 
Charlestown, Massachusetts, 
and died in New York City. 
After graduating from Yale 
at the age of nineteen, he 
studied art in England under 
Benjamin West. In 1832 he 
perfected the electric tele¬ 
graph, and in 1843 was 
granted an appropriation by 
Congress for a line between 
Washington and Baltimore. 
In 1844 this line was com¬ 
pleted,— the first successful 
electric telegraph on a large 
scale. 





THE ELECTRIC BELL 


449 


telegraph companies are now worked by means of currents 
from dynamo machines. 

555. The Signals are a series of sharp and light clicks 
separated by intervals of silence of greater or less dura¬ 
tion, a short interval between the 
clicks being known as a “ dot,” and 
a long one as a “ dash.” By a com¬ 
bination of “ dots ” and “ dashes,” 
letters are represented and words are 
spelled out. 

556. The Telegraph System described 
in the preceding sections is known 
as Morse’s, from its inventor. Fig¬ 
ure 478 illustrates diagrammatically 
the instruments necessary for one 
terminal station, together with the 
mode of connec¬ 
tion. The ar¬ 
rangement at the 
other end of the 
line is an exact duplicate of this one, 
the two sections of the battery being 
placed in the line, so that the negative 
pole of one and the positive pole of the 
other are connected with the earth. 

At intermediate stations the relay and 
the local circuit are connected with the 
line in the same manner as at a termi¬ 
nal station. 

557. The Electric Bell (Fig. 479) is 
used for sending signals as distinguished from messages. 
Besides the gong, it contains an electromagnet, having 
one terminal connected directly with a binding-post, and 



Figure 479 . — Elec¬ 
tric Bell. 



nal Instruments on 
Telegraph Line. 







450 


DYNAMO-ELECTRIC MACHINERY 


the other through a light spring attached to the armature 
(shown on the left of the figure) and a contact screw, 
with another binding-post. One end of the armature is 
supported by a stout spring, or on pivots, 
and the other carries the bent arm and 
hammer to strike the bell. Included 
in the circuit are a battery and a push¬ 
button B , shown with the top unscrewed 
in Fig. 480. 

When the spring E is brought into 
contact with J) by pushing (7, the cir¬ 
cuit is closed, the electromagnet attracts 
the armature, and the hammer strikes 
the gong. The movement of the arma¬ 
ture opens the circuit by breaking contact between the 
spring and the point of the screw; the armature is then 
released, the retractile spring at the bottom carries it 
back, and contact is again estab¬ 
lished between the spring and the 
screw. The whole operation is re¬ 
peated automatically as long as the 
circuit is kept closed at the push¬ 
button. A “ buzzer ” is an electric 
bell without the hammer and gong. 

Instead of two dry cells for ring¬ 
ing house bells, a small step-down 
transformer connected to the light¬ 
ing wires, with the bells in circuit 
on the low voltage side, gives satisfactory service (Fig. 
481). The bells need not be changed in any way, 
since the frequency of the current is too high to per¬ 
mit them to respond without the usual automatic circuit 
breaker. 



Figure 481 . — Trans¬ 
former for Ringing 
Bells. 




THE MICROPHONE 


451 


V. THE TELEPHONE 



Figure 482 . —-The Modern 
. Telephone. 


558. The Telephone (Fig. 482) consists of a horseshoe 
magnet 0 , both poles of which are surrounded by a coil of 
many turns of fine copper 
wire whose ends are con¬ 
nected with the binding- 
posts t and t. At right 
angles to the magnet, and 
not quite touching the 
poles, within the coils, is an 
elastic diaphragm or disk 
of soft sheet-iron, kept 
in place by the conical 
mouthpiece d. If the in¬ 
strument is placed in an 
electric circuit when the current is unsteady, or alternat¬ 
ing in direction, the magnetic field due to the helix, when 
combined with that due to the magnet, alters intermit¬ 
tently the number of lines of force which branch out from 
the poles, thus varying the attraction of the magnet for 
the disk. The result is that the disk vibrates in exact 
keeping with the changes in the 
current. 

559. The Microphone is a device 
for varying an electric current 
by means of a variable resistance 
in the circuit. One of its simplest 
forms is shown in Figure 483. It 
consists of a rod of gas-carbon 
A , whose tapering ends rest loosely in conical depressions 
made in blocks of the same material attached to a sound¬ 
ing board. These blocks are placed in circuit with a 



Figure 483 . — Microphone. 



















452 


D YNAMO-ELECTRIC MA CHINER Y 


battery and a telephone. While the current is passing, 
the least motion of the sounding board, caused either by 
sound waves or by any other means, such as the ticking 
of a watch, moves the loose carbon pencil and varies the 
pressure between its ends and the supporting bars. A 
slight increase of pressure between two conductors, resting 
loosely one on the other, lessens the resistance of the con¬ 
tact, and conversely. Hence, the vibrations of the sound¬ 
ing board cause variations in the pressure at the points 
of contact of the carbons, and consequently make cor¬ 
responding fluctuations in the current and vibrations of 
the telephone disk. 

560. The Solid Back Transmitter. — The varying resist¬ 
ance of carbon under varying pressure makes it a valuable 
material for use in telephone trans¬ 
mitters. Instead of the loose con¬ 
tact of the microphone, carbon in 
granules between carbon plates is 
now commonly employed. 

The form of transmitter exten¬ 
sively used for long distance work 
is the “solid back” transmitter 
(Fig. 484). The figure shows only 
Figur E] 484 . — Solid Back essen ti a l p ar t s i n section, minor 

details being omitted. M is the 
mouthpiece, and F and 0 the front and back parts of the 
metal case. The aluminum diaphragm D is held around 
its edge by a soft rubber ring. The metal block W has a 
recess in front to receive the carbon electrodes A and B. 
Between them are the carbon granules. The block E is 
attached to the diaphragm and is insulated from W ex¬ 
cept through the carbon granules. The transmitter is 
placed in circuit by the wires connected to W and E. 












Field Wireless Outfit of the United States Army. 
This can be set up and put into operation in seven minutes. 









Wireless Room in a Transatlantic Liner, 
















OSCILLATORY DISCHARGES 


453 


Provision is made for an elastic motion of the diaphragm 
and the block E. Sound waves striking the diaphragm 
cause a varying pressure between the plates and the car¬ 
bon granules. This varying pressure varies the resist¬ 
ance offered by the granules and so varies the current. 
The transmitter is in circuit in the line with the primary 
of a small induction coil, the secondary being in a local 
circuit with the telephone receiver. The induced currents 
in the secondary have all the peculiarities of the primary 
current; and when they pass through a receiver, it re¬ 
sponds and reproduces sound waves similar to those which 
disturb the disk of the transmitter. 

VI. WIRELESS TELEGRAPHY 

561. Oscillatory Discharges. —The discharge of any con¬ 
denser through a circuit of low resistance is oscillatory. 
The first rush of the discharge surges beyond the condi¬ 
tion of equilibrium, and the 
condenser is charged in the 
opposite sense. A reverse 
discharge follows, and so 
on, each successive pulse 
being weaker than the pre¬ 
ceding, until after a few 
surges the oscillations cease. 

Figure 485 was made from 
a photograph of the oscil- Fioure 485. -Oscillatory Dis- 

r ° r CHARGE. 

latory discharge of a con¬ 
denser by means of a very small mirror, which reflected 
a beam of light on a falling sensitized plate. Such alter¬ 
nating surges of high frequency are called electric oscil¬ 
lations. Joseph Henry discovered long ago that the 
discharge of a Leyden jar is oscillatory. 






454 


DYNAMO-ELECTRIC MACHINERY 


562. Electric Waves. — In 1887-1888 Hertz made the 
discovery that electric oscillations give rise to electric 
waves in the ether, know as Hertzian waves, which ap¬ 
pear to be the same as waves of light, except that they 
are very much longer, or of lower frequency. They are 
capable of reflection, refraction, and polarization the same 
as light. 

Evidence of these waves may be readily obtained by 
setting up an induction coil, with two sheets of tin-foil on 
glass, Q and Q\ connected with the terminals of the sec- 



Figure 486. — Electric Wave Transmitter. 


ondary coil, and with two discharge balls, F and F\ as 
shown in Fig. 486. So simple a device as a large picture 
frame with a conducting gilt border may be used to detect 
waves from the' tin-foil sheets. If the frame has shrunken 
so as to leave narrow gaps in the miter at the corners, 
minute sparks may be seen in a dark room breaking across 
these gaps when the induction coil produces vivid sparks 
between the polished balls, F and F'. The plane of the 
frame should be held parallel with the sheets of tin-foil. 
The passage of electric waves through a conducting circuit 
produces electric oscillations in it, and these oscillations 
cause electric surges across a minute air gap. 








CRYSTAL DETECTORS 


455 


563. The Coherer. — One of the earliest devices for the 
detection of electric waves is the coherer (Fig. 487). 
When metal filings are placed loosely between solid elec¬ 
trodes in a glass tube they offer a high resistance to the 
passage of an electric current; 
but when electric oscillations 
are produced in the neighbor¬ 
hood of the tube, the resistance 
of the filings falls to so small a value that a single voltaic 
cell sends through them a current strong enough to work 
a relay (§ 553). If the tube is slightly jarred, the filings 
resume their state of high resistance. A minute discharge 
from the cover of an electrophorus (§ 432) through the 
filings lowers the resistance just as electric oscillations 
do. It is thought that minute sparks between the filings 
partially weld them together and make them conducting. 

564. Crystal Detectors. — The coherer is now obsolete 
and more sensitive detectors have been discovered. The 
object aimed at in most of them is the rectification of the 
rapid oscillations from the receiving antenna or aerial wire, 
so as to secure a unidirectional discharge which will affect 
a telephone. On account of its high self-inductance, a 
telephone acts as a choke coil to high frequency electric 
oscillations and will not respond to them. It has been 
found that certain crystals, such as polished silicon, galena, 
and carborundum, possess a unilateral conductivity for 
electricity. A crystal of carborundum may have three or 
four thousand times as great conductivity in one direction 
as in the opposite for certain voltages. Hence, if a crystal 
detector is inserted in the oscillation circuit of a receiver, 
it rectifies the oscillations in a train of electric impulses, 
to which a telephone will respond with a sound correspond¬ 
ing in pitch to the number of impulses per second. 



Figure 487. — The Coherer. 





456 


DYNAMO-ELECTRIC MACHINERY 


The crystal is held in a conducting holder and is touched 
lightly by a metal point (Fig. 488). The brass cup shown 
in the figure holds the crystal securely by means of 



Figure 488. — Holder for Crys¬ 
tal Detector. 


three set screws. Another 
method of mounting is to 
embed the crystal in a soft 
alloy which melts at a low 
temperature. The contact 
wire can be moved about so 
as to find the sensitive spots 
in the crystal. 


565. The Audion is a very sensitive detector, depending for its 
action on the fact that electrons are thrown off from the negative end 
of an incandescent filament in an exhausted (or partly exhausted) 
bulb. If the bulb has supported in it a plate surrounding the fila¬ 
ment (Fig. 489), a single voltaic cell will send a (negative) current 
from its negative electrode to the negative end of the hot filament, 
thence through the space in the bulb to the metal plate, and out 
to the other pole of the voltaic 
cell. No current will flow unless 
the negative pole of the cell is 
connected to the negative of the 
filament. This arrangement is 
therefore an electric valve or rec¬ 
tifier, which lets electric impulses 
through in one direction and not 
in the other. Fleming calls it 
an “oscillation valve.” In the 
figure, oscillations in one direc¬ 
tion from the oscillation trans¬ 
former T will pass through the 
circuit, including the valve V and 
the telephone P, but not those 
in the other direction. 



Figure 489. — “ Oscillation 
Valve.” 


The audion is a modification of the “ oscillation valve ” of Fleming, 
which becomes a relay for the aerial oscillations to operate receiving 





















TRANSMITTING AND RECEIVING CIRCUITS 457 


telephones in a circuit with a battery (Fig. 490). In addition to the 
hot filament and the metal plate the audion has a “ grid” consisting 
of a coil of copper wire, which is one terminal of the circuit from 
the receiving helix. The 
other terminal of this cir¬ 
cuit is joined to the fila¬ 
ment. The negative of the 
adjustable battery B is 
joined to the negative end 
of the filament. The recti¬ 
fied train of impulses passes 
through from the hot fila¬ 
ment to the copper coil. 

The passage of these impulses 
causes similar impulses from 
the battery B to pass between 
the filament and the metal 
plate , and hence through the 
receiving telephone T. 



566. Transmitting and Receiving Circuits. — A simple 


tuned transmitting circuit 



Figure 491. — Transmitting 
Circuit. 

The magnetic effect of 
pulses is never reversed. 


for wireless telegraphy is illus¬ 
trated in Figure 491, where I 
is an induction coil, 0 a con¬ 
denser, S a spark gap, H a 
variable helix, A the aerial or 
antenna, and E the earth con¬ 
nection. 

Figure 492 is a correspond¬ 
ing simple receiving circuit. 
The receiving telephones are 
shown at T, the detector at D, 
and a variable condenser at 
0. These arrangements are 
capable of many variations, 
i rectified train of electric im- 
Hence they pass through the 

































458 


DYNAMO-ELECTRIC MACHINERY 



Figure 492. — Receiving 
Circuit. 


high resistance telephones and produce a distinct musical 
tone. Continued tones are interpreted as dashes and 
short ones as dots; together they 
make up either the Morse or the 
Continental alphabet. 

The circuits in commercial 
wireless telegraphy are much 
more elaborate than those shown 
(Fig. 493). To avoid interfer¬ 
ence between signals from differ¬ 
ent stations, it is necessary to 
tune the sending and receiving 
circuits to the same frequency. 
They are then sensitive to one 
frequency and not to others. 
For detailed information the reader is advised to consult 
technical books on wireless telegraphy. 

567. Uses of Wireless Telegraphy. — In less than thirty 
years after Hertz’s fundamental discovery, wireless teleg¬ 
raphy has grown to large proportions, especially for sig¬ 
nals between ships at sea and for international intercourse. 
Wireless telegraphy is in use between all steamships. 
They are thus in communication with one another and 
with stations on the land. Various government stations 
have been erected for the purpose of keeping each govern¬ 
ment in communication with the ships in its navy, and 
with other governments. Notable among these are the 
station in Paris, for which the Eiffel Tower is utilized to 
support the antenna, and the station in Arlington near 
Washington. Communication between these two stations 
is not difficult, and signals between them have been used 
to determine the difference of longitude between Paris 
and Washington. During the progress of this work, the 










Heinrich Rudolf Hertz (1857-1894) was born in Hamburg, 
and was educated for a civil engineer. Having decided to aban¬ 
don his profession, he went to Berlin and studied under Helm¬ 
holtz, and later became his assistant. In 1885 he was appointed 
professor of physics at the Technical High School at Karlsruhe, 
and while there he discovered the electromagnetic waves pre¬ 
dicted by Maxwell, who in the middle of the century had ad¬ 
vanced the idea that waves of light are electromagnetic in char¬ 
acter, In 1889 he was elected professor of physics at Bonn, 
where he died at the age of thirty-seven. Electromagnetic waves 
are called Hertzian waves in his honor. 





r 



Thomas Alva Edison was 

born at Milan, Ohio, in 1847. 
Beginning life as a newsboy, 
he has become the greatest 
American inventor. He per¬ 
fected duplex telegraphy, 
and invented among other 
things the carbon telephone 
transmitter, the microtasim- 
eter, the aerophone, the 
megaphone, the phonograph, 
the kinetoscope, and the in¬ 
candescent electric lamp. 


Guglielmo Marconi was 

born at Bologna, Italy, in 
1874. He studied in his 
native city, at Leghorn, and 
also, for a short time, in 
England. At the age of 
twenty-one he began his 
experiments in wireless teleg¬ 
raphy, and by 1895 was 
able to send messages across 
the English Channel. Since 
then his system has been so 
developed that marconigrams 
are sent across the Atlantic, 
and practically all important 
ships are equipped with wire¬ 
less apparatus. 









Wireless TElepbonY 4o9 


time of transmission of the signals between Paris and 
Washington was found to be 0.021 second. Signals are 
occasionally received at the Marconi Station, County Gal¬ 
way, Ireland, from stations many thousand miles away; 
for example, from Darien, San Francisco, and Honolulu. 

A.- Aerial 
A.G. • Anchor Gap 
H. M. - Mili- Ammeter 

O. H.- Oscillation Helix 
R. - Rotary Spark Gap 
T. • Transformer 

C. • Transmitting Condenser 

K. • Transmitting Key 
G. • Ground 
A.S.* Aerial Switch 
V. C. - Variable Condenser* 

L. C. • Loose-Coupled Turner 

D. • Detector 
F.C. - Fixed Condenser 

P. • Receivers 


Receiving Apparatus 


7 7c. 


Figure 493. — Commercial Transmitting and Receiving Apparatus.' 


568. Wireless Telephony. For the purpose of trans¬ 
mitting speech by wireless, it is necessary to have a 
source of energy that will transmit a persistent train of 
undamped waves. This may be accomplished either by 
means of an oscillating arc or by a high frequency al¬ 
ternator. These must emit continuous trains of waves 
with a frequency of 4000 or more per second. A special 
microphone carves the transmitted current and the train 
of waves emitted into groups of amplitudes corresponding 
with the sounds spoken into the microphone. The words 
are received with the usual telephonic receivers. 




































CHAPTER XV 


THE MOTOR CAR 

569. The Modern Motor Car or Automobile has come into 
such extensive use in the last few years that the principles 
of its construction and operation should be generally 
understood. Motor cars are usually classified according 
to the power which propels them, as electric, steam, and 
gasoline. Since the gasoline car is so much more widely 
used than either of the other two, it is the only one con¬ 
sidered in this chapter. 

570. The Gasoline Automobile uses the internal combus¬ 
tion engine (§ 380), the four-cycle type, for its motor. 
The number of cylinders varies from four to twelve, and 
the pistons , whatever their number, act on a common 
crank shaft . Figure 494 shows a four-cylinder engine and 
Figure 495 a six. Whatever the number of cylinders, 
the energy from the explosion is applied intermittently. 
The greater the number, the more nearly continuous is 
the stream of energy. 

In the four-cylinder engine there are two explosions 
for each revolution of the crank shaft, 180° apart. For a 
six, there are three, 120° apart; for an eight, there are 
four, 90° apart; and for a twelve, there are six, 60° apart. 
Figure 496 illustrates a twelve-cylinder engine or “ twin- 
six.” 

571. The Engine. —The vital part of the motor car is 
the engine, and constant and intelligent attention on the 

460 


THE ENGINE 


461 



Courtesy of Dodge Brothers 

Figure 494. — Cross Section of a Four-cylinder Engine. 



Courtesy of the Buick Company 

Figure 495. — Cross Section of a Six-cylinder Valve-in-Head Engine. 

























462 


THE MOTOR CAR 



part of the operator is necessary to secure smooth and 
uniform action. In § 380 the mode of action of a four¬ 
cycle engine is described, but if continuous and uninter¬ 
rupted action is to be secured a number of points must 
be observed : — 

(1) Since the explosion of the gaseous mixture heats 
the cylinder to a very high temperature, the operation of 


Courtesy of the Packard Company 

Figure 496. — One Side of a Twelve-cylinder Engine. 


the engine soon becomes impossible unless some cooling 
device is used. This is secured, except in the “ air¬ 
cooled” type of car, by the circulation of water about the 
cylinders and through a device called the radiator , where 
it is cooled by the action of a fan and the rapid radiation 
due to the large surface exposed. In some cases the 
water is circulated by a pump; in others, the so-called 
“ thermo-siphon ” system is used. By this system, the 
cold water entering the water-jacket from the bottom of 








THE ENGINE 


463 


the radiator forces up the hot water that is around the 
cylinders into the reservoir above the radiator, from 
which it flows through the radiator where it is cooled. 



Courtesy of the Cadillac Company 

Figure 497. — Front View of V-type Engine. 


Most “ eights ” and “ twelves ” are of this type with four or six cylinders 
placed in opposite rows. 


The reservoir above the radiator should always be kept as 
nearly full as convenient. 

(2) Every motor must be kept thoroughly lubricated. 
Practically all cars now use both the “pump” and 






464 


THE MOTOR CAR 


“ splash ” systems, whereby the oil is not only spattered 
about the inside of the engine by the rapidly revolving 
crank shaft, but it is also pumped to parts less likely to be 
reached by the splash system. Every engine has an oil 
gauge which should be constantly watched, as the explo¬ 
sions of the gas consume some of the oil, and the absence 
of lubricant causes “knocking” and laboring on the part 
of the motor. 

(3) Because of the incomplete burning of the carbon in 
the explosion, a gradual deposit forms on the pistons and 

points of the spark 
plugs. This accumu¬ 
lation of carbon may 
cause a fouling of the 
spark plugs to such 
an extent that they do 
not function, and the 
engine stops; or it 
may form sufficiently 
to hold fire between ex¬ 
plosions, and produce 
pre-ignition. A pound¬ 
ing or knocking in the 
engine is one of the 
indications of the presence of carbon. It may be removed 
by opening the engine and scraping the carbon off. 

(4) The proper mixture of the air and gasoline is neces¬ 
sary to the best action of the engine. This mixing is done 
by the carburetor (Fig. 498), a device through which the 
suction of the pistons draws air and gasoline in proper 
proportions for the several cylinders. The manifold is 
the tube that conveys the mixture from the carburetor to 
the different cylinders. Most cars have a carburetor 





THE ENGINE 


465 


adjustment on the dash, so that any desired mixture can 
be obtained. A richer mixture is desirable when starting 
the engine than after it has become warm, and it is also 
possible to operate on a thinner mixture at high speeds 
than at low. A car which has been running satisfactorily 
at twenty-five miles an hour on as thin a mixture as pos¬ 
sible will often stall when “ throttled down ” to ten or 
twelve miles an hour. The carburetor is often warmed 
by a pipe from the exhaust of the engine and sometimes 
it is partly surrounded by a water-jacket. 

(5) The gas is ignited by an electric spark which 
jumps between two metal points in the spark plug , which 
is placed at or near the head of the cylinder. This spark 



is furnished either by an induction coil connected with 
a storage battery or by a high-tension magneto (Fig. 
499) which is turned by a connection with the crank shaft. 
The crank shaft by suitable gearing also operates a timer , 











































466 


THE MOTOR CAR 


which connects the spark plugs successively and explodes 
the gas at the proper time. 

Ignition troubles are usually caused by foul spark 
plugs. When the action of the engine is jerky it shows 
that some cylinder.is “missing.” The one at fault can 
be ascertained by touching some metal part of the engine 
with the end of a screw-driver and holding another part 
of the metal of the screw-driver close to the spark plug 
connections. The plug where no spark jumps across is 
probably the one causing the trouble. 

572. The Storage Battery. — So little attention is re¬ 
quired by the storage battery that it is often too much 
neglected. It should be examined at least every two 
weeks and the plates covered with distilled water. It 
should be tested from time to time with the hydrometer 
(Fig. 60) and recharged at once if the density has fallen 
below 1.200. The electrolyte of a battery in good condi¬ 
tion has a density from 1.250 to 1.300. An idle battery 
will not remain charged but must have attention as often 
as once every two weeks. 

On long summer trips of continuous driving and 
also by rapid driving for a few hours a battery some¬ 
times becomes overcharged. This may be remedied by 
switching on the lights of the car for a while. In the 
winter season, on account of the difficulty of starting 
the car when cold, the battery is likely to be run 
down. This condition will be accentuated by the in¬ 
creased use of the lights. It will relieve the heavy 
drain on the battery to start the car by the use of 
the crank; at least it is advisable to turn the engine 
over a few times to get it well oiled before resorting to 
the starter. 


THE RUNNING GEAR 


467 


573. The Chassis (pronounced “shassy") is the name 
applied to the skeleton body of the car (Fig. 500), as 
distinguished from the hood , which incloses the engine, 
the tonneau , which is the rear seat division of a touring 
car, and the running gear , as the wheels are generally 





Figure 500. — A Typical Chassis. 


called. The chief care required by the chassis is its 
lubrication. It is fully supplied with grease cups which 
require constant “ turning up ” and filling. Grease 
cups which lubricate revolving parts require more fre¬ 
quent attention than those on joints and spring bolts. 

574. The Running Gear consists of the wheels and tires. 
The rear wheels are usually lubricated from the differen¬ 
tial (§ 578) and require practically no attention. The 
bearings of the front wheels are usually packed in grease, 
and at least once a year the wheels should be removed 
and the bearings cleaned and repacked in grease. 

The tires consist of a flexible inner tube, containing 
air under pressure, and a thick outer casing, sometimes 
called the shoe . Tire makers recommend a pressure of 
about twenty pounds for each inch of cross sectional 
diameter; that is, a four-inch tire should carry eighty 










468 


THE MOTOR CAR 


pounds’ pressure to the square inch; a four and a half, 
ninety pounds; and a five-inch tire, one hundred pounds. 
Less pressure may give more comfort in riding, but there 
is the danger that an excessive flattening of the tire may 
separate the layers of fabric and rubber. 

This applies to the heavy outer casing wherein lies the 
main expense in the maintenance of a car. Oil and tar 
are enemies of rubber and should be removed from the 
tire as soon as possible by means of a cloth dampened 
with gasoline. Rough roads should either be avoided or 
traversed at as low a speed as possible. Fast driving, 
especially in hot weather, is particularly hard on tires in 
that the tires become heated and disintegration sets in. 

A blow-out is caused by a weakening of the tire casing 
or shoe, through which the inner tube is forced out by 
the air pressure, exploding with a loud report. A punc¬ 
ture is caused by a nail, or some sharp instrument like a 
piece of glass cutting through the casing and making a 
small hole in the inner tube, through which the air es¬ 
capes gradually without “ blowing out ” the casing. 
Sometimes a leak occurs in the valve, which is delicately 
constructed, and the rubber washer of which may be¬ 
come defective through heat or age. The valve may 
then be unscrewed by reversing the little pointed cap 
which protects it and a new valve may be screwed in at 
slight expense. 

575. The Brakes.—All automobiles are provided with 
double brakes — the service brake, operated by the foot, 
and the emergency brake, usually operated by a hand lever. 
These brakes consist of steel bands lined with asbestos 
acting by friction on drums attached to the driving shaft 
or to the rear wheels. They should always be kept in 


THE CLUTCH 


469 



good condition and should always be applied gradually 
except in a case of great emergency. The clutch should 
always be thrown out when the brakes are applied. In 
some types of cars the clutch and service brake are on the 
same foot lever and in applying the brake the construction 
is such that the clutch is thrown out before the brake 
comes into action. 

576. The Clutch is a friction coupling connecting the 
crank shaft with the transmission shaft. There are many 
different forms, as the multiple disk, the cone, etc., but 


Figure 501. — Multiple Disk Clutch and Transmission. 

those that have proved the most satisfactory depend on 
friction. The clutch must always be thrown out in shift¬ 
ing the gears from 44 neutral,” in changing the gears in 
any way, and in stopping the car, and it should be let in 

















470 


TEE MOTOR CAR 


gently to prevent jerking. Figure 501 shows a section of 
one type of clutch and the transmission gears. 

577. The Transmission comprises all those parts which 
transmit power from the engine to the rear wheels, but the 
group of gear wheels just back of the clutch is usually re¬ 
ferred to as the transmission. Its function is to make 
changes in speed possible by various combinations of 
gears. The gasoline motor develops power in proportion 
to its speed, so that if great pulling power is required, a 
high speed of the motor must be combined with a low 
speed of the car, and this is obtainable only through a 
system of gears. In starting a car always begin in low 
gear, shifting to second when a moderate degree of speed 
has been attained, and not going into “ high ” until the 
car is well under way. 

578. The Differential.—The rear wheels of a car are 
the driving wheels and motion is communicated to them 
from the engine through the clutch, the transmission, the 



driving shaft, and finally through a device called the 
differential (Fig. 502). This is an ingenious assem¬ 
blage of gear wheels so connected as to permit the drive 










THE STARTER 


471 


wheels to rotate independently, as is necessary in turning 
a corner. The differential requires little attention, but 
must be examined occasionally to make sure that it is 
thoroughly oiled. 

The plan of the differential is such that one wheel may 
turn while the other is stationary, and for this reason on a 
slippery road it is necessary to place a chain on each drive 

wheel. If only one chain is used, the chain wheel may be 

standing still while the other one spins rapidly without 
securing any “ traction.” 

579. The Steering Device is a broad wheel and shaft 
carrying the throttle lever and the spark lever and connected 
with the front wheels by an 
endless screw working in a 
worm wheel (Fig. 503). 

It should turn readily, but 
should not be allowed to 
have too much play, as on 
it depends the control of 
the car. 

580. The Starter. —Most 
cars are now equipped with 
an electric starter, a small 
direct current motor oper¬ 
ated by the storage bat¬ 
tery. Pressing a spiral 
switch by means of a plug, 
usually in the floor board, 
closes the circuit, causing 
the armature to revolve. A suitable reduction gear con¬ 
nects the armature shaft with the crank shaft of the 
engine, thus turning it over and setting it in motion. 



Figure 503. 




472 


THE MOTOR CAR 


Before pressing the starter plug, the gear lever should 
always be put in neutral, the spark retarded, the throttle 
advanced, and the “ mixture ” in the carburetor enriched. 
The starting plug should be released immediately on the 
engine’s beginning to run. The spark should then be 
advanced, the motor throttled down to a moderate speed, 
and the carburetor adjusted. 

581. On the Road.—The two most important rules of 
the road are’“Safety First” and • Courtesy to All.” 
Different cities and towns have local regulations, but the 
driver who is always careful and courteous will save him¬ 
self the trouble of memorizing countless specific rules. 
Always be prepared for every one else doing the wrong 
thing. In turning corners drive slowly and thus avoid 
becoming an example under § 145. Do not try to climb 
steep hills on “high ” just because you may be able to do 
so, and do not descend hills at high speed. 

If the motor stops or “stalls,” as it is usually termed, 
the first thing to investigate is the gasoline supply. In 
nine cases out of ten lack of gasoline causes the stalling. 
Otherwise, some flaw in the ignition system, such as a 
broken wire or a short circuit, may cause the trouble. 
Sometimes the fan belt has worked loose so that the fan 
has ceased to function and the engine is overheated. This 
is usually detected by the boiling of the water in the water 
jacket. 

After stopping, it is best to set the emergency brake, 
even on level ground; but do not forget to release it 
before starting. Always put the gear lever in neutral on 
stopping, except that after stopping on a steep down grade, 
it is usually wise to throw the gear lever into reverse for 
safety’s sake, and on a steep upgrade, to throw it into low 


THE PEDESTRIAN 


473 


gear. But you should be particularly careful to put it 
back into neutral before attempting to start the car. 

The engine is a natural brake. So in descending a hill, 
throttle the engine down and leave the clutch in. The 
speed can then be governed easily by the service brake 
and the car be more completely under control. When de¬ 
scending very steep hills, it is well to go into second or 
even into first speed to brake the car. 

In night driving do not use bright head lights on ap¬ 
proaching another car; always turn them down to “ dim.” 
A bright light is blinding to the driver of the oncoming 
car and may cause a serious accident. 

In general, study the car, the plan of all the parts, their 
office, and their adjustment. Rattles usually come from 
loose nuts, squeaks from' empty grease cups. Look the 
car over often to see if everything is secure and in place. 
Inspect the gasoline, water, and oil supply before starting 
out from the garage. In this way you will have fewer 
accidents and less annoyance and expense. 

582. The Pedestrian. — In communities where motor 
cars are numerous, pedestrians should take the utmost 
care to avoid accidents. In crowded cities which have 
traffic officers at crossings, we should watch the signals of 
the officer, keeping on the sidewalk until he signals the 
traffic to stop. 

Where there is no officer the traffic usually keeps to the 
right. Hence we should look first to the left until halfway 
across, then to the right for the rest of the way. As we 
start across there is no danger of being hit from the right; 
but when halfway across, that is the side from which the 
danger comes. 

Asking for rides should be discouraged as a dangerous 


474 


THE MOTOR CAR 


proceeding. If the driver is unfriendly, we are completely 
at his mercy and he can take us where he will. If he is 
friendly, we are subjecting him to risk, because he is liable 
for any injury to us, whether in the car or in getting on 
or off. 

Courtesy, common sense, and obedience to traffic regu¬ 
lations are as important for pedestrians as for motorists. 


APPENDIX 

I. GEOMETRICAL CONSTRUCTIONS 

The principal instruments required for the accurate con¬ 
struction of diagrams on paper are the compasses and the 
ruler . For the construction of angles of any definite size the 

protractor (Fig. 
504) can be used. 
There are, how¬ 
ever, a number of 
angles, as 90°, 60°, 
and those which 
can be obtained 
from these by bi¬ 
secting them and 
combining their 
parts, that can be constructed by the compasses and ruler alone. 
A convenient instrument for the rapid construction of the 
angles 90°, 60°, and 30°, is 
a triangle made of wood, 
horn, hard rubber, or card¬ 
board, whose angles are 
these respectively. Such 
a triangle may be easily 
made from a postal card 
as follows: Lay off on the 
short side of the card (Fig. 

505) a distance a little less 
than the width, as AB. Separate the points of the compasses 
a distance equal to twice this distance. Place one point of the 
compasses at B, and draw an arc cutting the adjacent side at C. 

475 














476 


APPENDIX 


A 

Figure 506. 


Cut the card into two parts along the straight line BC. The 
part ABC will be a right-angled triangle, having the longest 
side twice as long as the shortest side, with the larger acute 
angle 60° and the 
smaller 30°. With 
this triangle and a 

straight edge the ^ 

majority of the con¬ 
structions required 
in elementary phys¬ 
ics can be made. 

Prob. 1. — To con¬ 
struct an angle of 90°. 

Let A be the ver- _ 

tex of the required B 
angle (Pig. 506). 

Through A draw the straight line BC. Measure off AD, any 
convenient distance; also make AE = AD. With a pair of 
compasses, using D as a center, and a radius longer than AD, 
draw the arc mn ; with Pas a cen¬ 
ter and the same radius, draw the 
arc rs, intersecting mn at F. Join 
A and F. The angles at A are right 
angles. 

Prob. 2. — To construct an angle 
of 60°. 

Let A be the vertex of the re- 
— quired angle (Pig. 507), and AB one 
of the sides. On AB take some 
convenient distance as AC. With 
a pair of compasses, using A as a center and AC as a radius, 
draw the arc CD. With C as a center and the same radius, draw 
the arc mn, intersecting CD at E. Through A and E draw the 
straight line AE ; this line will make an angle of 60° with AB. 



C 

Figure 507. 





GEOMETRICAL CONSTRUCTIONS 


477 


Prob. 3. — To bisect an angle. 

Let BAC be an angle that it is required to bisect (Fig. 508). 
Measure off on the sides of the angle equal distances, AD and 

AE. With D and E as centers 
and with the same radius, draw 
the arcs mn and rs, intersecting 
at F. Draw AF. This line 
will bisect the angle BAC. 

Prob. 4. — To make an angle 
equal to given angle. 

Let BAC be a given angle; 
Figure 508. it is re( l u i re( i to make a second 

angle equal to it (Fig. 509). 
Draw DE, one side of the required angle. With A as a cen¬ 
ter and any convenient radius, draw the arc mn across the given 
angle. With D as a center and the same radius, draw the 
arc rs. With s as a center and a radius equal to the chord of 




mn, draw the arc op, cutting rs at G. Through D and G 
draw the line DF. This line will form with DE the required 
angle, as FDE. 

Prob. 5. — To draw a line through a point parallel to a 
given line. 

Let A be the point through which it is required to draw 
a line parallel to BC (Fig. 510). Through A draw ED, 





478 


APPENDIX 


cutting BC at D. At A make the angle EAG equal to EDO. 
Then AG or FG is parallel to BC. 



Prob. 6. — Given two adjacent sides of a parallelogram, to com - 
plete the figure. 

Let AB and AC be two adjacent sides of the parallelogram 
(Fig. 511). With C as a center and a radius equal to AB, 


V} 



draw the arc mn. With B as a center and a radius equal to 
AC, draw the arc rs, cutting mn at D. Draw CD and BD. 
Then ABDC is the required parallelogram. 






CONVERSION TABLES 


479 


II. CONVERSION TABLES 
1. Length 


To reduce 


Multiply by 

To reduce 

Multiply by 

Miles to km. . . 



Kilometers to mi. . 

. 0.62137 

Miles to m. . . 

• 

. 1609.347 

Meters to mi. . . 

. 0.0006214 

Yards to m. . . 



Meters to yd. . . 

. 1.09361 

Feet to m. . . 



Meters to ft. . . . 

. 3.28083 

Inches to cm. 


. . 2.54000 

Centimeters to in. . 

. 0.39370 

Inches to mm. 


. . 25.40005 

Millimeters to in. . 

. 0.03937 


2. Surface 


To reduce Multiply by To reduce Multiply by 

Sq. yards to m. 2 . . . 0.83613 Sq. meters to sq. yd. . . 1.19599 

Sq. feet to m. 2 .... 0.09290 Sq. meters to sq. ft. . . 10.76387 

Sq. inches to cm. 2 . . . 6.45163 Sq. centimeters to sq. in. 0.15500 

Sq. inches to mm. 2 . 645.163 Sq. millimeters to sq. in. 0.00166 


3. Volume 


To reduce 

Multiply by 

To reduce 

Multiply by 

Cu. yards tom. 8 . . 

0.76456 

Cu. meters to cu. yd. 

. . 1.30802 

Cu. feet to m. 3 . . . 

. 0.02832, 

Cu. meters to cu. ft. 

. . 35.31661 

Cu. inches to cm. 3 . . 

. 16.38716 

Cu. centimeters to cu. 

in. 0.06102 

Cu. feet to liters . . 

. 28.31701 

Liters to cu. ft. . . , 

, . 0.03532 

Cu. inches to liters 

. 0.01639 

Liters to cu. in. . , 

. . 61.02337 

Gallons to liters . . . 

. 3.78543 

Liters to gallons 

. . 0.26417 

Pounds of water to liters 

. 0.45359 

Liters of water to lb. 

. 2.20462 



4. Weight 


To reduce 

Multiply by 

To reduce 

Multiply by 

Tons to kg. 

. . . 907.18486 

Kilograms to tons . 

0.001102 

Pounds to kg. 

. . . 0.45359 

Kilograms to lb. 

2.20462 

Ounces to g. . 


Grams to oz. . . 

0.03527 

Grains to g. . 

. . . 0.064799 

Grams to grains 

. 16.43236 












480 


APPENDIX 


5. Force, Work, Activity, Pressure 


To reduce Multiply by To reduce Multiply bj 

Lb.-weight to dynes, . 444520.58 Dynes to lb.-weight, 22496 x 10 -10 

Ft.-lb. to kg.-m. . . . 0.138255 Kg.-m. to ft.-lb. . . . 7.233 

Ft.-lb. to ergs . . 13549 x 10 8 Ergs to ft.-lb. . . 0*7381 X 10 -7 

Ft.-lb. to joules . . 1.3549 Joules to ft.-lb. . . . 0.7381 

Ft.-lb. per sec. to H.P. 18182 x 10 -7 H.P. to ft.-lb. per sec. . 550 

H.P. to watts • . . . 745.196 Watts to H.P. 0.001342 

Lb. per sq. ft. to kg. Kg. per m. 2 to lb. per 

per m. 2 . 4.8824 sq. ft. 0.2048 

Lb. per sq. in. to g. G. per cm. 2 to lb. per 

per cm. 2 . 70.3068 sq. in.0.01422 


Calculated for g = 980 cm., or 32.15 ft.-per-see. per sec. 


6. Miscellaneous 


To reduce Multiply by 

Lb. of water to U.S. gal. 0.11983 
Cu. ft. to U.S. gal. . . 7.48052 
Lb. of water to cu. ft. at 

4° C.0.01602 

Cu. in. to U.S. gal. . . 0.004329 
Atmospheres to lb. per 

sq. in. 14.69640 

Atmospheres to g. per 

cm. 2 . 1033.296 

Lb.-degrees F. to calories. 252 
Calories to joules . . . 4.18936 
Miles per hour to ft. per 

sec. 1.46667 

Miles per hour to cm. per 
sec. 44.704 


To reduce Multiply by 

U.S. gal. to lb. of water. 8.345 

U.S. gal. to cu. ft. . 0.13368 

Cu. ft. of water at 4° C. 

to lb. 62.425 

U.S. gal. to cu. in. . . 231 

Lb. per sq. in. to atmos¬ 
pheres . 0.06737 

G. per cm. 2 to atmos¬ 
pheres . 0.000968 

Calories to lb.-degrees F. 0.003968 

Joules to calories . . . 0.2387 

Ft. per sec. to miles per 

hour.0.68182 

Cm. per sec. to miles per 
hour. 0.02237 

















MENSURATION TABLES 


481 


m. MENSURATION RULES 


Area of triangle 
Area of triangle : 

Area of parallelogram 
Area of trapezoid 
Circumference of circle : 

Diameter of circle : 

Area of circle 

Area of ellipse 
Area of regular polygon 
Lateral surface of cylinder: 
Volume of cylinder 

Surface of sphere : 

Volume of sphere : 

Surface of pyramid •» 
Surface of cone / 
Volume of cone 


= \ (base x altitude). 

= \/s(s—a)(s—6)(s—c) where s=l (<z+6+c). 
= base x altitude. 

= Altitude x 1 sum of parallel sides. 

= diameter x 3.1416. 

(circumference 3.1416. 

I circumference x 0.3183. 

( diameter squared x 0.7854, 
t radius squared x 3.1416. 

= product of diameters x 0.7854. 

= £ (sum of sides x apothem). 

: circumference of base x altitude. 

= area of base x altitude. 
f diameter x circumference. 

14 x 3.1416 x square of radius, 
r diameter cubed x 0.5236. 

II of radius cubed x 3.1416. 

= | (circumference of base x slant height). 

= } (area of base x altitude). 



482 


APPENDIX 


IV. TABLE OF DENSITIES 


The following table gives the mass in grams of 1 cm. 3 of the sub¬ 
stance : — 


Agate. 


2.615 

Human body . . 

. . 

0.890 

Air, at 0° C. and 76 
pressure . . . 

cm. 

0.00129 

Hydrogen, at 0° C. 
76 cm. pressure 

and 

0.000081 

Alcohol, ethyl, 90%, 2C 

° c. 

0.818 

Ice. 


0.917 

Alcohol, methyl . . 


0.814 

Iceland spar . . 

. 

2.723 

Alum, common . . 


1.724 

India rubber . . 

. 

0.930 

Aluminum, wrought 


2.670 

Iron, white cast . 

. 

7.655* 

Antimony, cast . . 

. 

6.720 

Iron, wrought . . 

. 

7.698 

Beeswax .... 


0.964 

Ivory . 


1.820 

Bismuth, cast . . 

. 

9.822 

Lead, cast . . . 

. 

11.360 

Brass, cast . . . 


8.400 

Magnesium . . 

. 

1.750 

Brass, hard drawn . 


8.700 

Marble .... 


2.720 

Carbon, gas . . . 

. 

1.89 

Mercury, at 0° C. 

. 

13.596 

Carbon disulphide . 

. 

1.293 

Mercury, at 20° C. 

. 

13.558 

Charcoal .... 


1.6 

Milk. 


1.032 

Coal, anthracite . . 1 

Coal, bituminous . 1 

.26 to 1.800 
.27 to 1.423 

Nitrogen, at 0° C. 
76 cm. pressure 

and 

0.001251 

Copper, cast . . . 


8.830 

Oil, olive . . . 


0.915 

Copper, sheet. . . 

Cork. 

. . 8.878 

0.14 to 0.24 

Oxygen, at 0° C. and 76 
cm. pressure . . . 

0.00143 

Diamond .... 


3.530 

Paraffin . . . 0.824 to 0.940 

Ebony . 


1.187 

Platinum . . . 

. , 

21.531 

Emery. 


3.900 

Potassium . . . 


0.865 

Ether. 


0.736 

Silver, wrought . 

. # 

10.56 

Galena. 


7.580 

Sodium .... 


0.970 

German silver . . 

. 

8.432 

Steel . . . . . 


7.816 

Glass, crown . . . 


2.520 

Sulphuric Acid 

. 

1.84 

Glass, flint . . . 

3.0 to 3.600 

Sulphur .... 


2 ^33 

Glass, plate . . . 


2.760 

Sugar, cane . . 

. 

1.5. 

Glycerin .... 


1.260 

Tin, cast . . . 


7.290 

Gold. 



Water, at 0° C. . 


0.999 

Granite. 


2.650 

Water, at 20° C. . 

# , 

0.998 

Graphite .... 



Water, sea . . . 

, , 

1.027 

Gypsum, crys. > , 

. . 

2.310 

Zinc, cast . . . 






































GEOMETRICA L CONS Tit UCTION 


483 


V. GEOMETRICAL CONSTRUCTION FOR REFRACTION 
OF LIGHT 

The path of a ray of light in passing from one medium into 
another of different optical density is easily constructed geomet¬ 
rically. The following problems will make the process clear: 

First.—A ray from air into water. — Let MN (Fig. 502) be 
the surface separating air from water, AB the incident ray at 
B, and BE the normal. With B as a center and a radius BA 

draw the arcs mn and Cs. With 
the same center and a radius | of 
AB, (-J being the index for air to 
water), draw the arc Dr. Produce 
AB till it cuts the inner arc at D. 
Through D draw DC parallel to 
the normal EF, cutting the outer 
arc at C. Draw BO. This will 
be the refracted ray, because 

= % the index of refraction. 

Cr o 

When the ray passes from a 
medium into one of less optical 
density, then the ray is produced 
until it cuts the outer or arc of 
larger radius, and a line is drawn through this point parallel 
to the normal. The intersection of this line with the inner arc 
gives a point in the refracted ray which together with the 
point of incidence locates the ray. 

If the incident angle is such that this line drawn parallel to 
the normal does not cut the inner arc, then the ray does not 
pass into the medium at that point but is totally reflected as 
from a mirror. 

It is immaterial whether the arcs Dr and Cs are drawn in 
the quadrant from which the light proceeds, or, as in the 
figure, in the quadrant toward which it is going. 



Figure 512. 















484 


APPENDIX 


Second. — Tracing a ray through a lens. — Let MN represent 
a lens whose centers of curvature are C and C', and AB the 
ray to be traced through it (Pigs. 503, 504). Draw the normal, 



CB, to the point of incidence. With B as a center, draw the 
arcs mn and rs, making the ratio of their radii equal the index 
of refraction, f. Through p, the intersection of AB with rs, 
draw op parallel to the normal, C'B, and cutting mn at o. 
Through o and B draw oBD ; this will be the path of the ray 
through the lens. 

At D it will again m 

be refracted; to 
determine the 
amount, draw the 
normal CD and 
the auxiliary cir¬ 
cles, xy and uv, as 
before. Through 
the intersection of BD produced with xy, draw It parallel to 
the normal CD, cutting uv at l. Through D and l draw DH ; 
this will be the path of the ray after emergence. 

When the index of refraction is f, the principal focus of both 
the double convex and the double concave lens is at the center 
of curvature; for piano-lenses, it is at twice the radius of cui^ 
vature from the lens. 



N 

Figure 514. 











INDEX 


[Referenda art to pages.] 


Aberration, chromatic, 264 ; 

spherical, 235, 253. 

Absolute, scale of temperature, 
293 ; unit of force, 105; zero, 294. 
Absorption spectra, 268. 

Accelerated motion, 95. 

Acceleration, 93 ; centripetal, 100; 

of gravity, 124. 

Achromatic lens, 265. 

Action of points, 347. 

Adhesion, 10; selective, 11. 

Agonic line, 338. 

Air, brake, 87; compressibility of, 
73 ; compressor, 76 ; pressure of, 
68 ; weight of, 65. 

Air brake, 87. 

Air columns, laws of, 206. 

Airplane, 3, 113, 120, 325. 

Air pump, 76; experiments with, 
78. 

Airships, 81. 

Alternator, 431. 

Altitude by barometer, 71. 

Ammeter, 397. 

Ampere, 381. 

Amplitude, 138. 

Analysis of light, 263. 

Aneroid barometer, 70. 

Annealing, 15. 

Anode, 373. 

Antinode, 204. 

Arc, carbon, 442; inclosed, 443; 
open, 443. 

Archimedes, principle, 53. 

Armature, 421, 425; drum, 425. 
Artesian well, 50. 


Athermanous substances, 318. 
Atmosphere, unit of pressure, 69. 
Atmospheric electricity, 358. 
Attraction, electrical, 340; molecu¬ 
lar, 30, 35. 

Audion, 456. 

Aurora, 360. 

Automobiles, 1, 325, 460-474. 

Balance, 163. 

Balloons, 80. 

Barometer, aneroid, 70; mercurial, 
69 ; utility of, 70. 

Baroscope, 80. 

Battery, storage, 376; in a motor 
car, 466. 

Beam of light, 216. 

Beats, 195 ; number of, 196. 

Bell, electric, 449. 

Binocular, prism, 262. 

Blind spot, 261. 

Blow-out, of a tire, 468. 

Boiling, 303 ; in a motor car, 472. 
Boiling point, effect of pressure, 
305 ; on thermometer, 283. 

Boyle’s law, 74 ; inexactness of, 75. 
Brake, of a motor car, 468; use of 
engine as, 473. 

Bright line spectra, 268. 

British “tank,” 2, 104. 

Brittleness, 14. 

Buoyancy, 53; of air, 80; meas¬ 
ure of, 53. 

Caloric, 280. 

Calorie, 297. 


1 


2 


INDEX 


[References are to pages.] 


Camera, photographer’s, 259. 

Capacity, dielectric, 352; electro¬ 
static, 350; thermal, 297. 

Capillarity, 32; laws of, 33; re¬ 
lated to surface tension, 34. 

Capstan, 165. 

Carbon, in a motor car, 464. 

Carburetor, 464. 

Cartesian diver, 56. 

Cathode, 373 ; rays, 412. 

Caustic, 236. 

Cell, voltaic, 361; chemical action 
in, 363. 

Center, of gravity, 123; of oscilla¬ 
tion, 139 ; of percussion, 140; of 
suspension, 138. 

Centrifugal force, 133; illustra¬ 
tions of, 135 ; its measure, 134. 

Centripetal force, 133. 

Charge, residual, 353; seat of, 
353. 

Charles, law of, 293. 

Chassis, of a motor car, 467. 

Choke coil, 436. 

Chord, major, 197; minor, 197. 

Chromatic aberration, 264. 

Circuit, closing and opening, 363; 
divided, 397; electric, 363 ; trans¬ 
mitting and receiving, 457. 

Circular motion, 100. 

Clarinet, 205. 

Clinical thermometer, 285. 

Clutch, of a motor car, 469. 

Coherer, 455. 

Cohesion, 10. 

Coil, choke, 436; induction, 406; 
primary, 406; secondary, 407. 

Cold by evaporation, 303. 

Color, 271; complementary, 275 ; 
mixing, 273; of opaque bodies, 
271; of transparent bodies, 272 ; 
primary, 273. 

Commutator, 423. 

Composition of forces, 107; of 
velocities, 113. 


Compressibility of air, 73. 

Concave, lens, 249; mirror, 229 ^ 
focus of, 230, 249. 

Condenser, 351; office of, 408. 

Conductance, of electricity, 378; 
of heat, 309. 

Conductor, electrical, 343; charge 
on outside, 346; magnetic field 
about, 387. 

Cone clutch, 469. 

Conservation of energy, 153. 

Convection, 312; in gases, 313. 

Convex, lens, 246; mirror, 231; 
focus of, 230. 

Cooling system, in a motor car, 462, 
463. 

Coulomb, 348. 

Couple, 109. 

Crank shaft, in a motor car, 460. 

Critical angle, 244. ^ 

Crookes tubes, 412. 

Crystal detectors, 455. 

Crystallization, 35. 

Current, electric, 361; convection, 
313; detection of, 366; heating 
effects of, 385; induced by cur¬ 
rents, 403 ; induced by magnets, 
402; magnetic properties of, 387 ; 
mutual action of, 390; strength 
of, 381. 

Curvilinear motion, 99. 

Cyclonic storms, 71. 

Cylinders, in a motor car, 460-463. 

Daniell cell, 370. 

Day, sidereal, 23 ; solar, 22. 

Declination, magnetic, 338. 

Density, 58; of a liquid, 62; of a 
solid, 60; bulb, 62. 

Derrick, 165. 

Deviation, angle of, 241. 

Dew point, 307. 

Diamagnetic body, 328. 

Diathermanous body, 318. 

Diatonic scale, 197. 


INDEX 


3 


[References are to pages.] 


Dielectric, 351; capacity, 352; in¬ 
fluence of, 351. 

Differential, in a motor car, 467, 
470, 471. 

Diffraction, 278. 

Diffusion, 25, 28. 

Dipping needle, 337. 

Discharge, intermittent, 411; oscil¬ 
latory, 453. 

Dispersion, 263. 

Drum armature, 425. 

Dry ceU, 371. 

Dry dock, 57. 

Dryness, 307. 

Ductility, 12. 

Dynamo, 421; compound, 426; 
series, 425 ; shunt, 425. 

Dyne, 105. 

Earth, a magnet, 336. . 

Ebullition, 303. 

Echo, 186. 

Efficiency, 159. 

Effusion, 26. 

Elasticity, 36; limit of, 36; of 
form, 36 ; of volume, 36. 

Electric, bell, 449; circuit, 363; 
current, 361; current detection, 
366; motor, 426; railways, 430; 
telegraph, 447 ; waves, 454. 

Electrical, attraction, 340; distri¬ 
bution, 346; machines, 355; 
potential, 348; repulsion, 341; 
Resistance, 378; wind, 347. 

Electrification, 340; atmospheric, 
358; by induction, 344; kinds 
of, 341; simultaneous, 342 ; unit 
of, 348. f 

Electrode, 363, 377. 

Electrolysis, 373; laws of, 375; of 
copper sulphate, 373; of water, 374. 

Electrolyte, 362, 373. 

Electromagnet, 392; applications 
of, 394. 

Electromotive force, 365, 381; in¬ 


duced by magnets, 401; induced 
by currents, 403. 

Electrons, 419. 

Electrophorus, 354. 

Electroplating, 376. 

Electroscope, 342. 

Electrostatic, capacity, 350; in¬ 
duction, 344. 

Electrostatics, 340. 

Electrotyping, 376. 

Energy, 1, 148; conservation of, 
153 ; dissipation of, 153 ; kinetic, 
150; measure of, 151; potential, 
149 ; transformation of, 152. 

Engine, gas, 323; steam, 320; 
two-cycle, 325; four-cycle, 324, 
460-466. 

English system of measurement, 

22 . 

Equilibrant, 109. 

Equilibrium, 108; kinds of, 125; 
of floating bodies, 55; under 
gravity, 125. 

Erg, 145. 

Ether, 214. 

Evaporation, cold by, 303. 

Expansion, coefficient of, 289; 
of gases, 289 ; of liquids, 288; of 
solids, 287. 

Extension, 6. 

Eye, 259 ; defects of, 262. 

Falling bodies, 128, 130. 

Field, electrical, 387, 391; mag¬ 
netic, 333. 

Field magnet, 425. 

Floating bodies, 55. 

Fluids, 39; characteristics of, 39; 
pressure in, 41. 

Fluoroscope, 415. 

Flute, 205. 

Focus, 230; conjugate, 232; of 
lens, 249 ; of mirrors, 232. 

Foot, 18. 

Foot pound, 144. 


4 


INDEX 


\References are to pages.] 


Force, 5, 104; composition of, 107; 
graphic representation of, 107; 
how measured, 106; molecular, 
29; moment of, 160; parallelo¬ 
gram of, 110; resolution of, 111; 
units of, 105. 

Force pump, 86. 

Forced vibrations, 188. 

Fountain, siphon, 85; vacuum, 79. 

Four-cylinder engine, 460, 461. 

Fraunhofer lines, 268. 

Freezing, mixtures, 302; point, 283. 

Friction, 156; uses of, 158, 469. 

Fundamental, tone, 202; units, 23. 

Fusion, 299 ; heat of, 301. 

Gallon, 20. 

Galvanometer, d’Arsonval, 395. 

Galvanoscope, 366. 

Gas engine, 322-325, 460-466. 

Gas equation, 294. 

Gases, 40; compressibility of, 41; 
expansion of, 289; media for 
sound, 182; thermal conductivity 
of, 310. 

Gassiot’s cascade, 410. 

Gauge, water, 49. 

Geissler tube, 410. 

Grades, 170. 

Grain, 21. 

Gram, 21. 

Gramme ring, 424. 

Gravitation, 122; law of, 123. 

Gravitational unit of force, 105. 

Gravity, 122; acceleration of, 122; 
cell, 371; center of, 123; direc¬ 
tion of, 122 ; specific, 59. 

Hammer, riveting, 88. 

Hardness, 14. 

Harmonic, curve, 178; motion, 

101 . 

Harmonics, 204. 

Heat, 280; conduction of, 309 ; con¬ 
vection of, 312; due to electric 
current, 385; from mechanical 


action, 319; kinetic theory of, 
280; lost in solution, 302; me¬ 
chanical equivalent of, 320; 
measurement of, 297; nature of, 
280; of fusion, 301; of vaporiza¬ 
tion, 306; radiant, 315; related 
to work, 319; specific, 297; 
transmission of, 309. 

Heating by hot water, 312. 

Helix, 389 ; polarity of, 389. 

Holtz machine, 355. 

Hooke’s law, 37. 

Horizontal line or plane, 123. 

Horse power, 147. 

Humidity, 307. 

Hydraulic, elevator, 44; press, 42; 
ram, 51. 

Hydro-airplanes, cuts facing page 66. 

Hydrometer, 63, 466. 

Hydrostatic paradox, 47. 

Ice plant, ammonia, 304 .\/^ 

Images, by lenses, 250; by mirrors, 
225, 233 ; by small openingsT218. 

Impenetrability, 6. 

Impulse, 116. 

Incandescent lamp, 444. 

Inclination, 387. 

Inclined plane, 169; mechanical 
advantage of, 170. 

Index of refraction, 240. 

Indicator diagram, 322. 

Induced magnetism, 331. 

Induction, charging by, 345; coil, 
406; electromagnetic, 401; elec¬ 
trostatic, 344 ; motors, 440 ; self- 
induction, 405. 

Inertia, 7. 

Influence machine, 355. 

Insulator, 343. 

Intensity of illumination, 219. 

Interference, of light, 276; of 
sound, 194. 

Intervals, 196; of diatonic scale, 
198 ; of tempered scale, 199. 


INDEX 


5 


[Reference* are to pages.] 


Ions, 364. 

Isobars, 71. 

Isoclinic lines, 337. 

Isogonic lines, 338. 

Joseph Henry’s discovery, 405. 

Joule, 145. 

Joule’s equivalent, 320; law, 385. 

Kaleidoscope, 229. 

Keynote, 197. 

Kilogram, 21. 

Kilogram meter, 144. 

Kinetic energy, 150; measure of, 
151. 

Kinetic theory, 27; of heat, 280. 

Lag of current, 433. 

Lalande cell, 372. 

Lamp, arc, 442; gas-filled, 446; 
incandescent, 444; metal fila¬ 
ment, 445. 

Lantern, projection, 259. 

Law, Boyle’s, 74; Lenz’s, 404; 
Ohm’s, 378; of Charles, 293; of 
electromagnetic induction, 401; 
of electrostatic action, 342; of 
falling bodies, 130; of gravita¬ 
tion, 123 ; of heat radiation, 316 ; 
of magnetic action, 330; of ma¬ 
chines, 156; Pascal’s, 41. 

Laws, of motion, 117; of strings, 

201 . 

Leclanche cell, 371. 

Length, 17. 

Lens, 246 ; achromatic, 265; focus 
of, 248; images by, 250. 

Lenz’s law, 404. 

Lever, 161 ; mechanical advantage 
of, 162. 

Leyden jar, 352; theory of, 353; 
charging and discharging, 352. 

Lift pump, 85. 

Light, 214; analysis of, 263; 
propagation of, 216; reflection 


of, 223 ; refraction of, 238; speed 
of, 215 ; synthesis of, 264. 

Lightning, 358; rod, 359. 

Lines, agonic, 338; isoclinic, 337; 
of magnetic force, 333. 

Liquefaction, 299. 

Liquid, 4, 40; cohesion in, 11; 
compressibility of, 40; density 
of, 62 ; downward pressure, 45; 
expansion of, 288; in connected 
vessels, 49; medium for sound, 
182 ; surface level in, 49 ; surface 
tension in, 30; thermal con¬ 
ductivity of, 310; velocity of 
sound in, 185. 

Liter, 20. 

Local action, 367. 

Lodestone, 327. 

Longitudinal vibrations, 177. 

Loudness of sound, 192., 

Lubrication, of a motor car, 463, 464. 

Machine, 155; efficiency of, 159; 
electrical, 355; law of, 156; 
mechanical advantage of, 160; 
simple, 159. 

Magdeburg hemispheres, 79. 

Magnet, artificial, 328; bar, 328; 
electro-, 392; horseshoe, 328; 
natural, 327. 

Magnetic, action, 330; axis, 329; 
field, 333; lines of force, 333; 
meridian, 329; needle, 329; 
polarity, 329; substance, 328; 
transparency, 329. 

Magnetism, induced, 330; nature 
of, 332; permanent and tem¬ 
porary, 332; terrestrial, 336; 
theory of, 333. 

Magneto, in a motor car, 465. 

Magnets, 327. 

Major chord, 197. 

Malleability, 14. 

Manifold, in a motor car, 464. 

Manometric flame, 209. 




6 


INDEX 


[References are to pages.] 


Mass, 9; units of, 21. 

Matter, 1; properties of, 6; states 
of, 4. 

Mechanical advantage, 160. 

Mechanical equivalent of heat, 

320. 

Mechanics, of fluids, 39; of solids, 
104. 

Melting point, 299; effect of 
pressure, 301. 

Meter, 17. 

Metric system, 17. 

Micrometer, 174. 

Microphone, 451. 

Microscope, compound, 256; sim¬ 
ple, 255. 'V 

Minor chord, 197. 

Mirror, 225; focus of, 230; images 
by, 226, 233; plane, 225; 

spherical, 229. 

Mobility, 39. 

Molecular, forces, 29; motion, 
26; physics, 25. 

Moment, of a force, 160. 

Momentum, 116. 

Motion, 91; accelerated, 95; 
curvilinear, 99; harmonic, 101; 
molecular, 26; periodic, 101; 
rectilinear, 91; rotary, 91; 
uniform, 92; vibratory, 101. 

Motor, electric, 426; induction, 
440. 

Motor car, 1, 460-474. 

Multiple-disk clutch, 469. 

Musical, scales, 196; sounds, 191. 

Needle, dipping, 337; magnetic, 
329. 

Newton’s, laws of motion, 116; 
rings, 276. 

Nodes, 203. 

Noise, 191. 

Octave, 197. 

Ohm’s law, 378, 382. 


Opaque bodies, 214. 

Opera glasses, 258. 

Optical, center, 247; instruments, 
255. 

Organ pipe, 206. 

Oscillation, center of, 139 ; electric, 
360. 

Ounce, 22. 

Overtones, 204, 208. 

Partial tones, 204. 

Pascal, experiments, 67; principle, 
41. 

Pendulum, applications of, 140; 
laws of, 138; seconds, 141: 
simple, 136. 

Percussion, center of, 140. 

Period of vibration, 138. 

Periodic motion, 101. 

Permeability, 335. 

Phonodeik, 211. 

Photographer’s camera, 259. 
Photometer, 221. 

Photometry, 219. 

Physical measurements, 16. 

Physics, 1. 

Pigments, 275. 

Pistons, in a motor car, 460. 

Pitch, 191; limits of, 199; relation 
to wave length, 192; of screw, 
173. 

Plumb line, 123. 

Pneumatic appliances, 83. 

Points, action of, 347. 

Polarity of helix, 389. 

Polarization, 368. 

Polyphase alternators, 434. 

Porosity, 11. 

Potential, difference, 348; zero, 
349. 

Pound, 21. 

Power, 145. 

Pre-ignition, 464. 

Pressure, 41 ; of fluids, 39; at a 
point in fluids, 46 ; air, 65 ; down- 



INDEX 


7 


[References are to pages.] 


ward, 45; effect on boiling point, 
305 ; effeet on melting point, 301; 
independent of shape of vessel, 47 ; 
in tires, 467. 

Principle of Archimedes, 53. 

Prism, 242 ; angle of deviation, 243. 

Proof plane, 342. 

Properties of matter, 6. 

Pulley, 165 ; differential, 168 ; me- • 
chanical advantage of, 167 ; sys¬ 
tems of, 166. 

Pump, air, 76; compression, 76; 
force, 86 ; lift, 85. 

Puncture, of a tire, 468. 

Quality of sounds, 193; due to 
overtones, 193. 

Radiation, 315 ; laws of, 316. 

Radiator, in a motor car, 462. 

Radioactivity, 416. 

Radiometer, 315. 

Radium, 417. 

Rainbow, 266. . 

Rays of light, 216.4-^^ 

Reflection, diffus ed, 224; law of, 
'223; multiple, 228; of light, 
223; of sound, 186; regular 
223; total, 243. S • 

Refraction, cause of, 239; atmos¬ 
pheric, 243 ; laws of, 241. 

Regelation, 301. 

Relay, 448. 

Resistance, of air, 129; electrical, 
378; formula for, 380; laws of, 
379 ; unit of, 379. 

Resolution, of a force, 111; of a 
velocity, 113. 

Resonance, 188, 190. 

Resonator, Helmholtz’s, 191. 

Resultant, 107. 

Riveting hammer, 88. 

Roentgen rays, 414. 

Rotating field, 438. 

Running gear, of a motor car, 467, 
468. 


Scale, absolute, 293; diatonic, 
197; tempered, 198. 

Screw, 172; applications of, 173; 
mechanical advantage of, 173. 

Second, 22. 

Secondary or storage cell, 376. 

Seconds pendulum, 141. 

Self-induction, 405. 

Shadows, 217. 

Shoe, in a motor car, 467 

Sidereal day, 23. 

Sight, 260. 

Singing flame, 195. 

Siphon, 83 ; intermittent, 85. 

Six-cylinder engine, 460, 461. 

Solar day, 22. 

Solenoid, 389 ; polarity of, 389. 

Solids, 4; density of, 60; ex¬ 
pansion of, 287; thermal con¬ 
ductivity of, 309; velocity of 
sound in, 185. 

Solution, 34; saturated, 35; heat 
lost in, 302. 

Sonometer, 201. 

Sound, 176, 181; air as a medium, 
182; liquids as media, 182; 
loudness of, 192; musical, 191; 
quality of, 193; reflection of, 
186; sources of, 181; trans¬ 
mission of, 182; velocity of, 
184; waves, 183. 

Sounder, telegraph, 447. 

Spark lever, 471. 

Spark plug, 465. 

Specific gravity, 59 ; bottle, 62. 

Specific heat, 297. 

Spectroscope, 269. 

Spectrum, solar, 263; kinds of, 
268. 

Speed, 92 ; of light, 215. 

Speeds, of a motor car, 470. 

Spherical aberration, in mirrors, 
235 ; in lenses, 253. 

Spheroidal state, 303. 

Spherometer, 174. 



8 


INDEX 


[References are to pages.] 


Splash system, of lubrication, 464. 
Stability, 126. 

Stable equilibrium, 125. 

Stalling, of a gas engine, 472. 
Starter, in a motor car, 471. 

Starting resistance, 429. 

States of matter, 4. 

Steam, engine, 320; turbine, 322. 
Steelyard, 162. 

Storage cell, 376, 466; Edison, 378. 
Strain, 36. 

Strength, of an electric current, 
381; methods of varying, 383. 
Stress, 36. 

Strings, laws of, 201. 

Sublimation, 303. 

Submarine boat, 57. 

Surface tension, 30; illustrations 
of, 31. 

Suspension, center of, 138. 
Sympathetic vibrations, 189. 
Synthesis of light, 264. 

Telegraph, electric, 447; key, 
447; signals, 449; system, 449 ; 
wireless, 453. 

Telephone, 451. 

Telescope, astronomical, 257; 
Galileo’s, 258. 

Te mperature, 2 80; measuring, 281. 
Tempered scale, 198. 

Tempering, 15, 199. 

Tenacity, 12. 

Thermal capacity, 297. 
Thermometer, 282; clinical, 285 ; 

limitations of, 285 ; scales, 283. 
Thermo-siphon, system of cooling, 
462. 

Throttle lever, in a motor car, 471. 
Thunder, 358. 

Time, 22. 

Timer, in a motor car, 465. 

Tires, 467, 468. 

Tone, fundamental, 202; partial, 204. 

Torricellian experiment, 67. 


Transformers, 435; cut facing page 
439. 

Translucent bodies, 214. 

Transmission, of heat, 267; of 
power, 437; in a motor car, 469, 
470. 

Transmitter, 447, 452. 

Transparent bodies, 214. 

Transverse vibrations, 176. 

Trombone, 205. 

Tuning fork, 190. 

Turnbuckle, 174. 

Twelve-cylinder engine, 460, 462. 

“ Twin-six,” 460. 

Units, 16; of heat, 297; of length, 
17; of mass, 21; of time, 22. 

V-type engine, 463. 

Vacuum, Torricellian, 67. 

Vaporization, 302; heat of, 265. 

Velocity, 92; composition of, 113; 
of light, 215; of molecules, 27; 
of sound, 184; resolution of, 113. 

Ventral segments, 204. 

Vertical line, 123. 

Vibration, amplitude of, 138; 

complete, 138; forced, 188; 

longitudinal, 177; of strings, 
201; period of, 138; single, 138; 
sympathetic, 189; transverse, 
176. 

Viscosity, 39. 

Volt, 381. 

Voltaic cell, 361; electrochemical 
action in, 363. 

Voltameter, 381. 

Voltmeter, 396. 

Water, gauge, 49; supply, 50; 
waves, 180. 

Watt, 148. 

Wave motion, 177. 

Waves, 177; longitudinal, 179; 
electric, 454 ; length, 180; sound, 
183 ; transverse, 177 ; water, 180. 



INDEX 


9 


[References are to -pages.] 


Wedge, 172. 

Weight, 9, 122; of air, 65; varia¬ 
tion of, 124. 

Welding, cut facing page 16. 

Weston normal cell, 382. . 

Wheatstone’s bridge, 391.-=^—^ 
Wheel and axle, 164; mechanical 
advantage of, 164. 

Wheels, of a motor car, 467. 


Whispering gallery, 188. 

* Wireless telegraphy, 453 ; teleph¬ 
ony, 459. 

Work, 143; units of, 144; useful, 
159; wasteful, 159. 

X-rays, 414. 

Yard, 18. 

Zeppelin, 81, 82. 







































































































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